"Spherical Tuples of Hilbert Space Operators"
(Indian Institute of Technology, Kanpur)
Abstract: We discuss a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on reproducing kernel Hilbert spaces. We further use these characterizations to describe various spectral parts including the Taylor spectrum. We also find a criterion for the Schatten $S_p$-class membership of cross-commutators of spherical $m$-shifts. We show, in particular, that cross-commutators of non-compact spherical $m$-shifts cannot belong to $S_p$ for $p \le m$. This is a joint work with Dmitry Yakubovich.
Date: Wednesday, July 1, 2015
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.