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Talk: Seminormal Operators

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Talk: Seminormal Operators

Cornelia Michlits

May 11, 2020

Start Mo 11 May 2020 2.30pm via Zoom:

https://tuwien.zoom.us/j/95714000580?pwd=a0QvZ2t1RlpnaWsyRzNxaGo4OFcyUT09

Abstract

For a bounded linear operator S on a Hilbert space that does not commute with its adjoint, the value of the selfcommutatorD=S∗S−SS∗ can be observed for further in- vestigation. OperatorsS with the property thatDis semidefinite, are calledseminormal.

Among others the vector-valued unilateral shift will serve as an example. Analogously to normal operators, known from functional analysis, we will derive some basic statements for the spectral radius and numerical range. Seminormal operators became interesting when looking at spectral mapping results, especially the fact that the two-dimensional Lebesgue measure of the spectrum is positive. This is the consequence of Putnam’s theorem.

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