Elcim Elgun, Pure Mathematics Department, University of Waterloo
"The Construction a West Compactication of Z"
Abstract:
Given
a
locally
compact
group
G,
a
compact
semigroup
S
is
called
a
semigroup
compactication
if
it
contains
a
dense
homomorphic
image
of
G.
We
study
the
question
of
extending
continuous
bounded
functions
on
G
to
its
various
semigroup
compactications.
In
particular
we
are
interested
in
the
largest
semigroup
compactication
of
G
associated
with
unitary
representations,
which
we
will
denote
by
Ge.
In
this
talk
we
will
restrict
our
attention
to
Z.
Our
aim
is
to
construct
a
compact
subsemigroup
of
L1[0;
1]
as
a
closure
of
Z.
The
construction
depends
on
an
idea
of
West,
which
implies
that
this
semigroup
is
a
quotient
of
Ze.
This
is
a
strong
indication
of
the
algebraic
and
topological
complexity
of
Ze.