REGISTRATION: click  here  to register, and to arrange accommodation.
Accommodation at preferential rates ranging from GBP35.00 to GBP65.00 per
person per night (depending on availability), at hotels close to the
department, can be arranged, provided sufficient notice is given.

Click here for travel information.

Participants are invited to post their titles and abstracts at
http://at.yorku.ca/cgi-bin/amca/submit/cakn-01

Submitted abstracts may be viewed at
http://at.yorku.ca/cgi-bin/amca/cakn-01

There is a registration fee of £25, payable on arrival,
which is waived for research students and  participants
from the Ukraine, Turkey or third world countries.

There is a possibility of some financial support for research students.
Please inquire.

The organizers gratefully acknowledge support from the London Mathematical Society.

To accommodate the number of speakers, the schedule allows 30 or 45 minutes
for talks, with 5 minutes for discussion and break between talks.
The talks will take place in

Room J11on the 6th floor of the Hicks Building, University of Sheffield.

LIST OF PARTICIPANTS
The TITLES AND ABSTRACTS of talks (in alphabetical order by author)
will appear below, as they become available.

I. Alayande, Unisa, South Africa
G.R. Allan, Cambridge, England
J.W. Baker, Sheffield, England
G. Dales, Leeds, England
S. Ferri, Universidad Nacional Autonoma de Mexico
M. Filali, Oulu, Finland
J. Galindo, Univ. Jaume I, Castellón, Spain.
F. Ghahramani, Manitoba, Canada
F. Gourdeau, Laval, Canada and Newcastle, England
N. Hindman, Howard Univ., USA
K.-H. Hofmann, Darmstadt, Germany
R.D. Kopperman, City Univ. of New York, USA
A.T. Lau, Alberta, Canada
J.D. Lawson, Baton Rouge, USA
P. Milnes, Western Ontario, Canada
M. Mislove, Tulane Univ., USA
W. Moran, Flinders Univ., Australia
I. Namioka, Univ. of Washington, USA
M. Neufang, Carleton Univ., Canada
A. Pears, England
A. Pourabbas, Newcastle, England
I. Protasov, Kiev, Ukraine
W.A.F. Ruppert, Vienna, Austria
D. Salinger, Leeds, England
P. Salmi, Sheffield, England
D. Strauss, Hull, England
A. Ulger, Koch Univ., Istanbul
T. West, Trinity College, Dublin
G. Willis,  Newcastle, Australia
Y.G. Zelenuk, Kyiv Taras Shevchenko Univ., Ukraine

TITLES and ABSTRACTS in alphabetical order by author.

G.R. ALLAN        The group of invertibles of a Fréchet algebra

ABSTRACT: There will be a brief introduction to some ideas on
`stable inverse-limit sequences' (G.R. Allan,  Stable inverse-limit sequences,
with application to Fréchet algebras, Studia Math.
121(3) (1996), 277--308). These ideas will be applied to study the
group of invertible elements in a Fréchet algebra.

H.G. DALES     John Pym, Arens regularity, and some developments

ABSTRACT:   Let A be a Banach algebra. Then the second dual space A''
is a Banach algebra for two Arens products.
The algebra A is Arens regular  if the two products coincide on
A''.   More generally  let us introduce two topological centres of
A'$:  A is Arens regular if both these centres are equal to A'', and,
at the other extreme, strongly Arens irregular if  both are equal to
A itself, regarded as a subset of A'$.

John Pym made important contributions to this theory; I shall briefly
recall some of the early results,including those of John. Several other
people at the meeting also have theorems in this area. I shall then discuss
a selection of recent developments, extensions, and examples. These new
results are taken from a joint memoir written with Tony Lau; if colleagues
wish to be given a copy of this memoir in Sheffield, it would be helpful if
you let me know in advance.

The  new developments concentrate on the regularity of Beurling algebras.

S. FERRI        The WAP-compactification of a SIN-group

ABSTRACT:  A semigroup compactification of a (Hausdorff) topological group G
is a pair (X,f), where X is a semigroup with a compact Hausdorff
topology and f:G --> X is a continuous homomorphism with dense
image such that all right translations x --> xy are continuous in
X and the left translations y --> f(s)y are continuous in X for
all s in G. In this talk we shall be interested in two semigroup
compactifications of G: the LUC-compactification, luc(G),
which is the
largest semigroup compactification of G (any other is a natural
quotient), and the WAP-compactification, wap(G), which is the largest
semigroup compactification of G in which the product is continuous
in both variables separately.

In general wap(G) need not be very large, as there are examples of
groups whose WAP-compactification is a singleton. However, in this
talk we shall show that this is not the case when G is a
SIN-group. More precisely, we shall show that, if we regard
wap(G) as a quotient of luc(G) and denote the quotient
map by p, then, when G is a SIN-group, there
exists a dense open subset of luc(G)-G consisting of points of
unicity for p of cardinality 2^2^k(G), where k(G)
denotes the compact covering number of G.

M. FILALI        On actions of a locally compact group on its LUC- and WAP-compactifications

ABSTRACT: Let G be a locally compact group.
The mapping lambda_x defined on G by lambda_x(g)=gx is known to be
injective on G for each x in the LUC-compactification
 UG of G when UG is given the right topological
semigroup structure. We study this property in the
WAP-compactification of G. We also look at the injectivity
of the mapping rho_x defined on G by rho_x(g)=xg.

J. GALINDO          On the Stone-Weierstrass theorem for group-valued functions

ABSTRACT: In this talk we shall be looking for Stone-Weierstrass-type theorems for
groups of continuous group-valued functions. Our approach to the problem will be marked by the
 concept of constructive group introduced by Sternfeld (Dense subgroups of
C(K)-Stone-Weierstrass-type theorems for groups, Constr. Approx. 6 (1990) ) that is based
on the fact that a vector subspace of C(X, R)
 stable under composition with certain maps  is automatically a subalgebra. A
 characterization of locally compact constructive groups will be presented and,
 as a particular case, we shall show that a locally compact connected group is constructive
(and thus satisfy a suitable version of the Stone-Weierstrass theorem) if and only if it contains no
compact subgroup or, what is  equivalent by virtue of Iwasawa's theorem, if and only if it
decomposes as the product of a finite family of subgroups topologically isomorphic to R.

F. GHAHRAMANI     Approximate weak amenability, multipliers and derivations of Segal algebras

ABSTRACT: Let  G  be a locally compact group,  L^1(G)  be the group algebra and  S^1(G)
be a Segal subalgebra of  L^1(G).  We show that when  G  is a SIN group  S^1(G)  is
approximately weakly amenable (previously we had this result under the additional assumption
that  G  was amenable).  For a compact group  G  we characterize multipliers and derivations from
the Lebesgue-Fourier algebra LA(G) into itself and into its second dual and we show that  LA(G)  is Arens regular.  This is joint work with Tony Lau.

N. HINDMAN       John and beta(N)

ABSTRACT: I intend to reminisce about the times, many years ago, when
John and I were discovering how badly noncommutative the maximal groups
in the smallest ideal of beta N are.  There is another related story
that I won't hint at now, because the hint would give the story
away.

K.H. HOFMANN       The Structure of Abelian Pro-Lie Groups
(coauthor: S.A. Morris)

ABSTRACT: A  pro-Lie group is a projective limit of a projective
system of  finite dimensional Lie groups. A
prodiscrete group is a complete abelian
topological group in which the open normal subgroups form a
basis of the filter of identity neighborhoods. It is shown here
that an abelian pro-Lie group is a product of (in general
infinitely many) copies of the additive topological
group of reals  and of an  abelian pro-Lie group
of a special type; this last factor has a compact connected
component, and a characteristic closed subgroup which is a
union of all compact subgroups; the factor group
modulo this subgroup is pro-discrete and free of nonsingleton
compact subgroups. Accordingly, a connected abelian pro-Lie
group is a product of  a family of copies of the reals and
a compact connected abelian group. A topological group is called
compactly generated if it is algebraically generated by a
compact subset, and it is called almost connected
if the factor group modulo its identity component
is compact. It is further shown that a  compactly generated
abelian pro-Lie group has a characteristic almost connected
locally compact subgroup which is  a product of a finite number
of copies of the reals  and a compact abelian group such that
the factor group modulo this characteristic subgroup is a
compactly generated prodiscrete group without nontrivial
compact subgroups. It is likely that such a group is a finitely
generated free discrete group, as is the case if it is first countable,
but we have no proof for the general case.

R.D. KOPPERMAN      Universal partial metrizability

ABSTRACT: It can be shown that many standard topological structures
essentially evidence the existence of a partial metric yielding them,
which are valued in a quantale, and the latter can be assumed stably
compact. Among these are: topologies, quasiproximities, quasiuniformities,
and pairwise completely regular bitopological spaces. We discuss this
equivalence and, as time allows, completions and other resulting notions.

J.D. LAWSON          Free constructions for topological semigroups

ABSTRACT: A topological semigroup S with identity e is said to be
freely locally generated if for every continuous local homomorphism
defined on a neighborhood N of e into a topological semigroup T,
there exists a unique continuous homomorphism h:S to T that agrees
with the local homomorphism on some neighborhood of e.   It is a standard fact
that a connected, locally connected topological group is freely locally
generated if and only if it is its own universal cover.  But in general
the theories of free local generation and of universal covering diverge
for topological semigroups.  In this talk we give some results and open
problems concerning the problem of constructing a freely locally generated
semigroup for a given topological semigroup or local semigroup.
 

A.T. LAU        Semigroup compactifications of locally compact groups

ABSTRACT: In this talk, I will survey the contributions of John on semigroup
compactifications of locally compact groups leading to our collaborations.

P. MILNES        Classification and discrete cocompact subgroups of
                                 nilpotent connected Lie groups

ABSTRACT: After a brief discussion of the situation for groups of dimension < 7,
most of the talk deals with one infinite family of 7-dimensional groups,
the discrete cocompact subgroups of its members (when such subgroups exist),
and their associated flows and C*-algebras.

M. MISLOVE      Domains, probability measures and quantum theory

ABSTRACT: Domains originated in attempts to give semantic models for
programming langauges, but about ten years ago, it became clear that
domain theory had insights to offer in many other areas. In particular,
the work of Abbas Edalat showed that domains could provide new approaches
to such areas as integration. One of the accomplishments of domain theory
that has received a lot of attention recently is its model of
probabilistic computation. This requires giving a domain-theoretic
presentation of the probability measures on a domain. In this talk, I'll
describe how this is done, and point out how some classical results can be
interpreted using domains. In addition, I'll decscribe some new results
showing how domains arise in models of quantum computation - this last is
recent work of Abramsky, Coecke and Martin at Oxford.

M. NEUFANG    Topological Centres Everywhere

ABSTRACT: In 1951, R. Arens showed that for any Banach algebra A, there are two
canonical ways of extending the product in A to its bidual. It turns
out that these products coincide for some class of algebras -- called
Arens regular -- which contains all C^*-algebras, but in general are
different. A natural way of measuring the (non-) regularity of A is to
consider the sets of elements in the bidual for which left (resp. right)
multiplication with respect to both products is the same, called the first
(resp. second) topological centre.
  I will present a unified approach that I developed in order to determine
these centres for various algebras arising in Abstract Harmonic Analysis,
such as the group algebra L_1(G) and the measure algebra M(G) for a locally
compact group G. The latter solves a conjecture made by Ghahramani and Lau
in 1994. I shall also show how these techniques can be applied to answer a
question on automatic boundedness of module homomorphisms on von Neumann
algebras raised by Hofmeier and Wittstock in 1997. I will furthermore
present:
- an application to semigroup compactifications related to the work of
Filali, Lau, Protasov, and Pym;
- the first example of a Banach algebra which equals its first but not its
second topological centre, which is in close connection to the recent work
of Dales and Lau;
- a tensor product version of the topological centre in the framework of
operator spaces.
  The talk aims at offering a panorama view of the colourful circle of ideas
around the 'topological centre' -- a view which we owe to John Pym to a
great extent.

I. PROTASOV       Coronas of Balleans

ABSTRACT:  A ballean is a triple (X,R,B) where X, R are nonempty sets and,
for all x from X, r from R,  B(x,r) is a subset of X which is called a ball
of radius r around x.
    Let (X1, R1, B1),  (X2, R2, B2) be balleans.  A mapping f from X1 to X2 is
called coarse if, for every r1 from R1 there exists  r2 from R2 such that
f(B1(x,r1)) is  contained in B2(f(x),r2) for every  x from X. A bijection f
is called an isomorphism if f and its inverse are coarse.
We show that the balleans (with the isomorphisms defined above) can be
considered as the asymptotic counterparts of uniform topological spaces. On
the ballean stage the part of continuous functions play slow oscilating
functions. We define a corona of  ballean as a generalization of Higson's
corona and a counterpart of Stone-Cech compactification.

W.A.F. RUPPERT   Compactification lattices of subsemigroups of SL(2,R)

ABSTRACT: This talk presents recent results about the structure of topological
semigroup compactifications of closed connected submonoids with
dense interior of SL(2,R). For a large class of such semigroups explicit constructions
yielding all possible topological semigroup compactifications are
given and the structure of the compactification lattice is determined.

D. STRAUSS        Chains of rectangular semigroups in beta(N).
(coauthors: N.Hindman and Y.Zelenuk)

I was first inspired to work in beta(N) by a talk in which John showed
that every maximal group in the smallest ideal of beta(N) contained copies
of the free group on 2^c generators. This amazed and fascinated me, and I have been
working on beta(N) ever since. I shall discuss the existence of another kind of
large semigroup in beta(N) - a semigroup which consists of a chain of c
rectangular components, each with 2^c elements.

A. ULGER        A short proof of the Glicksberg-Host-Parreau theorem.

ABSTRACT:  Let G be a locally compact abelian group, L1(G) be its group
algebra and M(G) be its measure algebra. Fix a measure m in
M(G). The Glicksberg-Host-Parreau Theorem states this: The ideal
L1(G)*m is closed in L1(G) iff the measure m is the
product of an invertible measure and an idempotent measure.
Only one proof of this theorem is known [Ann. Inst. Fourier 23
(1978),143-164] and it is very long and very sophisticated.
In this talk we present a very short (about 2-3 pages), self-contained
and elementary proof of this important theorem. Moreover our proof
also applies to some other Banach algebras such as the
Fourier algebra A(G) of a locally compact amenable group G.

G. WILLIS          Factorisation in finite codimensional ideals of group algebras

ABSTRACT: Let G be a locally compact group and let L^1(G) be the group convolution algebra of G.
Then for each closed cofinite ideal I in L^1(G) there are a closed left ideal L with a right bounded
approximate identity and a closed right ideal R with a left bounded approximate identity such that
I = L+ R. Consequently, every element of I is a sum of two products.

The proof of this claim uses a random walk on G to prove a convolution estimate in L^1(G).
This estimate is then used to define the ideals L and R and their approximate identities.

Y.G. ZELENYUK      Group operations on homogeneous spaces

ABSTRACT: It is well known that not all homogeneous spaces
admit a structure of a topological group and even a structure of a
group with continuous left shifts. I shall show that every countably
infinite homogeneous regular space admits a structure of any
countably infinite group with continuous left shifts.
 

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