Edward Kissin London Metropolitan University

Operator Lipschitz functions, Boyd indices and applications

Abstract:

We will discuss Operator J-Lipschitz functions for symmetrically normed ideals J. The smoothness of these functions depends on the Boyd indices of the ideals. We will consider the notion of interpolation spaces and why we need these spaces to describe the smoothness of J-Lipschitz functions. Additionally, we will try to examine some applications:

1. Distance to normal elements in C^*-algebras,
2. Gateaux and Fréchet differentiability of operator functions,
3. Actions of J-Lipschitz functions on the domains of derivations.

Realizing that this is too ambitious for a 1-hour talk, we will try not to get bogged down in too many details while, nevertheless, giving a comparatively full picture of this part of the theory of Operator Lipschitz functions.