Probabilistic Operator Algebra Seminar: Differentiability of operator functions

Seminar | September 4 | 3:45-5:45 p.m. | 748 Evans Hall

 Anna Skripka, University of New Mexico

 Department of Mathematics

Study of operator smoothness was initiated in the 50's. Since then it has substantially expanded in scope and methods in response to various problems in perturbation theory. The first order operator differentiability is well understood. In particular, it is known that the set of functions differentiable with respect to the Schatten $S^p$-norms, $p$ >1, can be described in terms of smoothness properties of scalar functions and is wider than the set of functions differentiable with respect to the operator norm or $S^1$-norm. The higher order differentiability was known for a limited set of functions, We will discuss new results that significantly extend the sets of higher order Frechet and Gateaux $S^p$-differentiable functions, $p$ >1. Our results are based on recent advances in theory of generalized multilinear Schur multipliers. The talk is based on joint work with Christian Le Merdy.