Linear Analysis Seminar

Date: March 27, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Martijn Caspers, TU Delft

Title: Non-commutative Lipschitz and commutator estimates

Abstract: In the 1940's Krein asked the question whether Lipschitz functions f: R -> C are also operator Lipschitz functions in the sense that the mapping B(H)_sa -> B(H): x -> f(x) is Lipschitz. The answer to this question is negative unless additional smoothness assumptions are imposed on f. On the other hand if the uniform norm on B(H) is replaced by the Schatten Lp-norm then every Lipschitz function is operator Lipschitz (Potapov-Sukochev 2010). In this talk we give a sharp proof of this result through so-called end-point estimates (weak L1-estimates and BMO-estimates). In order to achieve this we further develop the theory of Markov dilations and De Leeuw theorems. This is joint work with D. Potapov, F. Sukochev and D. Zanin.