17:00
Compactness properties of operator multipliers
Abstract
The Schur product is the commutative operation of entrywise
multiplication of two (possibly infinite) matrices. If we fix a matrix
A and require that the Schur product of A with the matrix of any
bounded operator is again the matrix of a bounded operator, then A is
said to be a Schur multiplier; Schur multiplication by A then turns
out to be a completely bounded map. The Schur multipliers were
characterised by Grothendieck in the 1950s. In a 2006 paper, Kissin
and Shulman study a noncommutative generalisation which they call
"operator multipliers", in which the theory of operator spaces plays
an important role. We will present joint work with Katja Juschenko,
Ivan Todorov and Ludmilla Turowska in which we determine the operator
multipliers which are completely compact (that is, they satisfy a
strengthening of the usual notion of compactness which is appropriate
for completely bounded maps).