## Linear Analysis Seminar

Date: November 17, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Anna Skripka, University of New Mexico

Title: Schur multipliers in perturbation theory.

Abstract: Schur multipliers and their generalizations have been actively studied for over a century. Classical linear Schur multipliers act on matrices as entrywise multiplications; multilinear Schur multipliers act by some intricate products. After recalling finite dimensional Schur multipliers, we will concentrate on their generalizations to multilinear transformations arising in infinite dimensional perturbation theory and consider an application to approximation of operator functions. In particular, we will discuss sharp conditions for Schatten class membership of remainders of approximations [1]. The affirmative case relies on the approach to Schur multipliers without separation of variables emerging from [3] and addressed in the nonself-adjoint case in [2]. [1] "Multilinear Schur multipliers and applications to operator Taylor remainders", with D. Potapov, F. Sukochev, and A. Tomskova, Adv. Math., 320 (2017), 1063-1098. [2] "Estimates and trace formulas for unitary and resolvent comparable perturbations", Adv. Math., 311 (2017), 481-509. [3] "Spectral shift function of higher order", with D. Potapov and F. Sukochev, Invent. Math., 193 (2013), no. 3, 501-538.