Laurent Marcoux, Department of Pure Mathematics, University of Waterloo
“The complete boundedness property for amenable operator algebras
One
of
the
most
intriguing
problems
in
the
theory
of
C*-algebras
stems
from
a
1955
paper
of
R.V.
Kadison
who
asked
whether
every
continuous
representation
of
a
C*-algebra
into
the
space
B(H)
of
bounded
operators
on
a
Hilbert
space
is
necessarily
similar
to
a
*-representation.
It
was
shown
by
U.
Haagerup
that
a
representation
of
a
C*-algebra
A
is
similar
to
a
*-representation
if
and
only
if
it
is
completely
bounded.
One can extend Kadison's problem as follows: Let A be an operator algebra and T be a continuous homomorphism of A into B(H) for some Hilbert space H. Is T necessarily completely bounded?
We
discuss
recent
progress
on
this
question
in
the
case
where
A
is
an
amenable
operator
algebra.
This
is
joint
work
with
Raphael
Clouatre
(University
of
Manitoba).
MC 5417