Operator Holder Functions with respect to Lp-norms, 0<p≤∞


Jinghao Huang


University of New South Wales


Wed, 31/07/2019 - 12:00pm


RC-4082, The Red Centre, UNSW


The study of operator Holder functions has a long history and plays an important role in the perturbation theory of linear operators on a Hilbert space. The starting point is the so-called Powers--Strømer inequality [Comm. Math. Phys. 1970] (and its generalization, the so-called Birman--Koplienko--Solomjak inequality [IVUZM, 1975]). Over the past decades, many mathematicians enlarged the classes of functions or the quasi-norms for which the inequality holds. Aleksandrov and Peller [JFA, 2010] showed Holder functions are not necessarily operator-Holder. However, it was unknown whether the simplest example of Holder functions, the fractional power functions, are operator-Holder for every Lp-norm or not before being proved by E. Ricard recently  [Adv. Math. 2018]. After reviewing the background material, I will sketch Ricard's proof and present the joint work with F. Sukochev and D. Zanin, which extends several existing results. 

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