Parasar Mohandy, Indian Institute of Technology
"Space of completely bounded Lp multipliers and its pre-dual"
Let
G
be
a
locally
compact
group.
G.
Pisier
considered
the
operator
space
structure
(oss)
on
Lp(G)
by
developing
operator
space
complex
interpolation.
In
this
oss
one
can
define
completely
bounded
Lp(G)
multipliers.
It
is
natural
to
ask
whether
the
space
of
completely
bounded
multipliers
on
Lp(G)
denoted
by
Mcbp
(G)
is
strictly
contained
inside
Mp(G),
the
space
of
multipliers
on
Lp(G).
For
p
=
1
and
2
it
can
be
shown
that
these
two
spaces
coincide.
In
this
talk
we
will
see
that
Mcbp
(G)
(
Mp(G)
for
any
infinite
locally
compact
abelian
group
G.
In
the
process
one
can
get
the
cb
version
of
Herz's
multiplier
homomorphism
theorem.
It
is
well
known
that
pre-dual
of
Mp(G)
can
be
identified
with
Figa-Talamanca-Herz
algebra
Ap(G).
We
will
address
the
question
of
pre-dual
of
Mcbp
(G).