ANNOUNCEMENT

**2004 Canadian Symposium on Abstract Harmonic
Analysis**

to be held at the

University of Western Ontario

May 17-18, 2004

Organized by

B. Forrest, Z. Hu, T. Miao, P. Milnes (milnes at
uwo.ca)

The schedule of talks
starts at 9:00 am, May 17 and ends at 4:10 pm, May 18. One hour talks
will be given by Jean-Paul Pier and John Pym.

Conference venue: The
talks will take place in Middlesex College 105,

near top-centre of the campus map.
(Here is a slightly different, but printable map ; here
is a

map of the relevant part of London .)

Travel to London and UWO: See http://jdc.math.uwo.ca/directions.php

(prepared by a member of my department) and UWO's

http://communications.uwo.ca/western/about_directions.html

For those going to COSY: Brian Forrest
<beforres@math.uwaterloo.ca> will organise a van to take people to
Waterloo on May 18, if sufficient
interest is expressed; contact him as soon as possible if you are
interested. Also, the Via Rail and Greyound websites say that, on
May 18, there are trains from London to Kitchener at 5:25 and 8:35 pm
(5/4 hr trip) and a bus at 5:15 pm (3/2 hr trip).

Accommodation:

One accommodation option is Essex Hall, click on
'Bed and Breakfast' at

http://www.uwo.ca/hfs/cs/
(where you make all the arrangements yourself).

Others can be arranged.

At Essex Hall, we have a block of 40 rooms reserved
until April 16, when any

unclaimed rooms become available to the public at large. When making an
on line

reservation for Essex Hall, you must choose one of

Economy Rate (no breakfast, no
cleaning) $29.00, and

Full Service Rate (continental
breakfast, daily clean) $43.50.

However, you can change
your choice when you arrive. You can also choose the

economy rate and then go to the breakfast nook in Essex Hall and pay
à la carte.

The breakfast at Essex Hall is 'continental',

- 1 bread item (toast, bagel, cereal, muffin),

- 1 fruit item,

- coffee, tea, juice, milk.

A hot breakfast is
available from 7:30 am at Lucy's in Somerville House,

which is on the way to Middlesex College from Essex Hall (see the map).

You can also look at http://www.has.uwo.ca/hospitality/eateries/eateries.cfm

The Conference Dinner will be held
at the Dragon Court Restaurant

in the evening of May 17 ($15/person).

The organizers acknowledge
support from the Fields Institute.

Announcement in the
CMS Notes February/04, p. 42.

SCHEDULE OF TALKS

ABSTRACTS **OF TALKS**

will appear below, as they become
available.

Monday, May 17 |

9:00-9:25 Colin C. Graham,
epsilon-Kronecker sets in discrete abelian groups. 9:30-9:55 Cédric Delmonico, Atomisation process for convolution operators on some locally compact groups. 10:00-10:25 Mehdi Sangani Monfared, On a class of Banach algebra extensions of the generalized Fourier algebras that split strongly. 10:30-10:50 Coffee 10:50-11:15 A.T. Lau, The centre of the second
conjugate algebra of the Fourier algebra for 11:20-11:45 F. Ghahramani, More on approximate amenability. 11:50-12:15 N. Hindman, Discrete n-tuples in beta(D). 12:20-1:45 Lunch 1:45-2:10 Z. Hu, A "Kakutani-Kodaira theorem" for von Neumann algebras on locally compact groups. 2:15-2:40 Keith Taylor, Smoothness of tight frame
generators. 3:15-3:35 Coffee 3:40-4:35 John Pym,
Some uses of second duals in harmonic analysis. 4:40-5:05 Yong Zhang, Approximate diagonals of Segal
algebras. 5:10-5:35 Ebrahim Samei, Approximately local derivations. 7:00 Dinner at the Dragon Court
Restaurant, 931 Oxford St. E., 453-8888 |

Tuesday, May 18 |

9:00-9:30 Vladimir
Pestov, Some recent links between topological transformation groups,
geometric functional analysis, and Ramsey theory. 9:35-10:05 M. Neufang, Aspects of quantization in abstract harmonic analysis. 10:10-10:30 Coffee 10:30-11:25 Jean-Paul Pier, Harmony fosters Beauty and Amenability. 11:30-12:10 E. E. Granirer, The Fourier-Herz-Lebesgue algebras Arp = Ap intersection Lr. 12:15-1:45 Lunch 1:45-2:10 Monica Ilie, Completely bounded Fourier algebra homomorphisms. 2:15-2:40 N. Spronk, On representations
of measures in spaces of completely bounded maps. 2:45-3:10 Wojciech Jaworski , Ergodic and mixing
probability measures on locally compact groups. 3:45-4:10 J. Galindo, Interpolation sets and some of
the harmonic analysis they should involve. 4:15 Coffee |

Abstracts:

Jean-Paul Pier, Harmony fosters
Beauty and Amenability.

John Pym, Some uses of second duals
in harmonic analysis.

Cédric
Delmonico, Atomisation process for convolution operators on some
locally compact groups.

Abstract: Let G be a locally compact group and 1 < p < infty. A
p-convolution operator on G is a bounded operator on L^p(G) which is
commuting with the left translation. The set of all p-convolution
operators on G, denoted by CVp(G), is a Banach algebra. There is a
injective homomorphism of the space of the bounded measures of G into
CVp(G), defined by the convolution of the functions on L^p(G) with
bounded the measure.

We say there is an atomisation process for the
convolution operators on G if there is a net (L_alpha) of endomorphisms
of CVp(G) which is converging to id such that L_alpha(T) have discrete
support, for all alpha. Moreover, we want to keep the control of the
norm and the support of L_alpha(T). In his thesis,

N. Lohoué have proved the existence of such atomisation process
on locally compact abelian groups

using structure theorems. I will give a constructive proof of existence
of atomisation process for a large class of locally compact groups. In
particular, we can approximate bounded mesures with discrete mesures, on
R^n, T^n, O(2) or the Heisenberg group.

Jorge Galindo, Interpolation sets and some of the harmonic analysis they should involve.

Abstract: Two types of questions
related to the existence of interpolation sets, an object of study in
Harmonic Analysis for more than 80 years, will be examined in this
talk: which groups admit interpolation sets in abundance and which
have none at all (the ubiquity and existence problems). While trying to
capture some of the general features, we shall focus on two types of
interpolation sets: I_0-sets and Sidon sets or, what is the same,
interpolation sets for the the algebra of almost periodic
functions and interpolation sets for the Fourier-Stieltjes algebra.

With the aid of well-known theorems of Rosenthal,
and Bourgain, Fremlin and Talagrand it is easy to see that a Polish
group G has no X-interpolation set (X being the uniform
closure of the above algebras of functions) if and only if the
spectrum of this algebra is Rosenthal compact (i.e. contained in the set
of functions of thefirst Baire class on some Polish space). These
topological arguments tie the existence of interpolation sets with
the structure of some weakly almost periodic compactifications (the Bohr
and Eberlein compactifications) and of spaces of matrix
coefficients of unitary representations. While this will provide
reasonable characterizations of locally compact groups with no I_0-sets,
it remains unclear which locally compact groups have no Sidon sets.

The ubiquity problem will be put in connection with
Rosenthal's ell^1-theorem and a version of this theorem in the
setting of locally compact groups will be presented. This links the
ubiquity problem for Sidon and I_0-sets with the kind of uniformity
the group receives from some of its (weakly) almost periodic
compactifications and with the existence of unitary
representations generating von Neumann algebras with
specificfeatures.

Fereidoun
Ghahramani, More on approximate amenability.

ABSTRACT.In this talk first I will review some background from the
paper, F.Ghahramani and R.J.Loy, Generalized notions of amenability,
J.Functional Analysis, 208(2004)229-260.Then I intend to present more
recent developments on approximate amenability such as:

1. The equivalence of the three notions, approximate amenability,
weak* approximate amenability and approximate conractibility;

2. approximate amenability of the James algebra;

3. Approximate weak amenability of every Symmetric Segal algebra
on an amenable group.

Colin
C. Graham, epsilon-Kronecker sets in discrete abelian groups.

(Based on joint work with K.E. Hare and T.W. Körner)

Abstract: Let 0 < epsilon < 2. A closed subset E of the
discrete abelian group Gamma is

``epsilon-Kronecker'' if for every continuous function f: E
--> T there exists x in the dual of Gamma
with |<gamma,x> - f(gamma)| < epsilon for all gamma
in E. These sets have the following properties when epsilon <
sqrt 2:

(i). E is I_0 (and the interpolating discrete measures can be
chosen in

any open subset when the dual of Gamma is connected).

(ii). The step length in an epsilon-Kronecker set goes to
infinity.

(iii). Previously known results about cluster points of E -
E and E + E

from Hadamard setsare extended to sums and differences of
epsilon-Kronecker sets.

(iv). Sums of epsilon-Kronecker sets are U_0 sets if
the number of terms is small relative

to epsilon and can be all of the group if the number of terms is large.

(v). For each epsilon > 0, there are epsilon-Kronecker
sets in the natural

numbers that are not finite unions of Hadamard (lacunary) sets.

Additionally,

(vi). When epsilon < 2, E does not contain arbitrarily long
arithmetic progressions.

E.
E. Granirer, The Fourier -Herz -Lebesgue algebras Arp = Ap
intersection Lr.

N.
Hindman, Discrete n-tuples in beta(D).

Abstract: Everyone learns in the crib
that any infinite subset of a Hausdorff space contains an infinite
discrete subspace. In the course of investigating some Ramsey Theoretic
results,

we established the following theorem:

Let X be a
Hausdorff topological space and assume that for each i,j in
omega, one has x_{i,j} in X such
that x_{i,j} neq x_{l,m}
whenever (i,j) neq (l,m). There exists an infinite subset M in omega such that x_{i,j} : i,j in M is discrete if
and only if {y in X:
some injective sequence in X converges to y} is finite. In particular, if X = beta(D) for an infinite discrete
space D, there exists an
infinite subset M in omega such that {x_{i,j} : i,j in M} is discrete.

After consulting with several experts we were
surprised to find out that the above theorem appears to be new. This
result raised the following question:

Let k in N. For which Hausdorff spaces X is it true
that whenever Gamma is an
injective function

from omega^k to X, there must exist some M in omega^{omega} such
that Gamma[M^k] is discrete?

For k = 1 the answer is ``all of them''.
And for k = 2, the theorem tells us that the answer is ``those for which
there are only finitely many points which are the limit of injective
sequences''. For larger values of k we are not able to answer this
question. However, we do show that the answer includes beta(D) for
infinite discrete spaces D.

Z. Hu,
A "Kakutani-Kodaira theorem" for von Neumann algebras on locally
compact groups.

Abstract. Let G be a locally compact group. In this talk, we present a
decomposition theorem for the

von Neumann algebras L_infty(G) and VN(G). We show how the exploration
for such a unified

approach for this dual pair of Kac algebras has led to a generalized
Kakutani-Kodaira theorem on the

local structure of G.

Monica
Ilie, Completely bounded Fourier algebra homomorphisms.

Abstract: Given a locally compact group G, the Fourier and
Fourier-Stieltjes algebra are defined as spaces of coefficient functions
associated with continuous unitary representations of $G$. In the
same

time, they can also be looked at as preduals of certain von Neumann
algebras and, consequently, they have a natural operator space structure.

It is known that, for abelian groups, there is a
deep connection between Fourier algebra homomorphisms and piecewise
affine maps between their underlying groups. We explore this fact from
the point of view of operator spaces, for general locally compact
groups. In joint work with Nico Spronk we extend a result of B. Host to
the class of locally compact groups that are amenable as discrete. This
represents a continuation of previous work done by the speaker in
the discrete case.

Wojciech
Jaworski, Ergodic and mixing probability measures on locally
compact groups.

Abstract: A probability measure mu on a locally compact groups G is
called ergodic (resp., mixing) if for every varphi in L^1_0(G) the
sequence \frac1n\sum_{i=1}^n\varphi *\mu^i (resp., varphi *\mu^n)
converges to zero in L^1(G). In general, mixing is strictly
stronger than ergodicity. We will discuss a long outstanding conjecture
that under a certain natural condition these two concepts are
equivalent.

A.T.
Lau, The centre of the second conjugate algebra of the Fourier
algebra for

infinite products of groups.

Abstract: In this talk, I shall report on a recent joint work with
Viktor Losert on the centre of the second conjugate algebra of the
Fourier algebra A(G) of a locally compact group G for an infinite
product of locally compact groups.

Mehdi
Sangani Monfared, On a class of Banach algebra extensions of the
generalized Fourier algebras that split strongly.

Abstract: In 1983, Lau introduced a new class of Banach algebras (later
called Lau algebras)

and studied in details certain direct sums of these algebras. In
this talk we show

that how persuing the same ideas will lead to a class of strongly
splitting extensions

of the generalized Fourier algebras A_p(G). Among other things we
discuss the

spectrum, bounded approximate identities, minimal idempotents, and the
Jacobson radical

of these extensions.

M.
Neufang, Aspects of quantization in abstract harmonic analysis.

ABSTRACT: Our aim is to give an overview of our recent
contributions to various aspects of 'quantization' in abstract harmonic
analysis -- where this (very fashionable) word has two meanings for us:

1. the use of operator space theory in the study of classical objects
in harmonic analysis;

2. the investigation of non-commutative counterparts of these objects
arising through the replacement of functions by operators.

We shall illustrate this programme by discussing the
following topics (throughout, G denotes a locally compact group).

1.1 Amenability theory. Z.-J. Ruan showed that the canonical
operator space structure of the Fourier algebra A_2(G) is crucial
for understanding its amenability properties -- by proving that A_2(G)
is operator amenable if and only if the group G is amenable (this
equivalence fails in the realm of classical amenability, as shown by
B.E. Johnson). We extend Ruan's theorem to the case of the
Figa-Talamanca--Herz algebras A_p(G), for p in (1, infty), endowed with
an appropriate operator space structure. The construction of the latter
requires the concept of non-hilbertian column operator spaces, as
developed recently by A. Lambert and G. Wittstock.

This is joint work with A. Lambert and V.
Runde.

1.2 Representation theory. We present a common
representation-theoretical framework for various

Banach algebras arising in abstract harmonic analysis, such as the
measure algebra M(G) and the completely bounded multipliers of the
Fourier algebra M_{cb} A_2(G). The image algebras are intrinsically
characterized as certain normal completely bounded bimodule maps on
B(L_2(G)). The study of our representations reveals intriguing
properties of the algebras, and provides a very simple description of
their Kac algebraic duality.

Part of this is joint work with Z.-J. Ruan and N.
Spronk.

2.1 Quantized convolution. The space T(L_2(G)) of trace class operators
is usually considered as the non-commutative version of L_1(G) on
the level of Banach spaces. We show that this analogy may be
extended to the Banach algebra level by

introducing a new product on T(L_2(G)) which parallels convolution of

functions.

2.2 Harmonic operators. In the context of the representation model as
described in 1.2, we study an operator version of the classical
Choquet-Deny equation (for a fixed probability measure on G), the
solutions of which we refer to as harmonic operators. We show that the
space of harmonic operators is naturally equipped with the structure of
a non-commutative von Neumann algebra, and completely describe its
structure as a W*-crossed product over the classical harmonic functions.

This is joint work with C. Cuny and W. Jaworski.

Vladimir
Pestov, Some recent links between topological transformation
groups, geometric functional analysis, and Ramsey theory.

Abstract. We will survey properties of topological groups of
transformations determined by oscillations of functions on phase spaces
(such as the extreme amenability, or the fixed point on compacta
property) and discuss their relationship with geometric functional
analysis and structural Ramsey theory, paying attention to a number of
concrete examples. In particular, we will discuss a reformulation of the
distortion property of the Hilbert space in terms of the infinite
unitary group, and show that it makes sense for great many `infinite
dimensional' groups and their homogeneous spaces in the context of
infinite combinatorics. We will survey some open problems.

Volker
Runde, (Non-)amenability of the Fourier algebra.

Abstract: We show that the Fourier algebra A(G) of a locally compact
group G is amenable if and only if G has an abelian subgroup of finite
index. This talk is based on joint work with Brian Forrest.

Ebrahim
Samei, Approximately local derivations.

Abstract: We initiate the study of certain linear operators from a
Banach algebra A into a Banach A-bimodule X, which we call approximately
local derivations. We show that when A is a C*-algebra, a Banach algebra
generated by idempotents, a semisimple annihilator Banach algebra, or
the group algebra of a SIN or a totally disconnected group, bounded
approximately local derivations from A into X are derivations. This, in
particular, extends a result of B. E. Johnson that ``local derivations
on C*-algebras are derivations" and provides an alternative proof of it.

N.
Spronk, On representations of measures in spaces of completely
bounded maps.

Abstract: Representations of the measure algebra M(G) of a locally
compact group G on spaces of operators on B(H) (itself the von Neumann
algebra of bounded operators on a Hilbert space H) have been studied by
Stormer, Ghahramani, Neufang, Smith and the presenter. I plan to
present on some work in progress where I study representations of
certain compactifications of G in spcaes wCB(B(H)) (normal completely
bounded maps on B(H)).

Ross Stokke, Amenable
representations and coefficient subspaces of Fourier-Stieltjes
algebras.

Abstract: The theory of amenable representations was first
developed in 1990 by M.E.B. Bekka and has since enjoyed the
attention of many authors. I will present characterizations of amenable
representations of locally compact groups, G, in terms of associated
coefficient subspaces of the Fourier-Stieltjes algebra, B(G), and in
terms of associated von Neumann and C^*-algebras. I will introduce
Fourier and reduced Fourier-Stieltjes algebras associated to
arbitrary representations, and will discuss amenable

representations in relation to these algebras. Some illustrative
(counter-)examples will also be presented.

Keith
Taylor, Smoothness of tight frame generators.

Abstract: We will explore the connection between the structure of a
'dilation' matrix and the degree of

smoothness that an associated tight frame generator may have.

Yong
Zhang, Approximate diagonals of Segal algebras.

Abstract: A proper Segal algebra is never amenable so it
never has a bounded approximate diagonal. But it may have an (unbounded)
approximate diagonal. We will discuss when such an approximate diagonal
exists.