CB-norm approximation of derivations by elementary operators

Ilja Gogic (Trinity College Dublin)

Tuesday 3rd March, 2015 16:00-17:00 Maths 326

Abstract

We often try to understand the structure of operators and spaces on which they act in terms of approximation by finite rank maps. On C*-algebras A, however, it is natural to regard two-sided
multiplication maps x \mapsto a x b as basic building blocks (instead of rank one operators). We can therefore try to approximate a more general map on A, one that preserves ideals, by finite sums of
two-sided multiplication maps, that is, by elementary operators. In this talk I will consider the problem of description of those derivations of C*-algebras that can be approximated by elementary operators in the completely bounded norm. This is a joint work in progress with Richard Timoney (Trinity College Dublin).