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Marko Kocic: The spectral theorem for normal operators and applications

Time: Fri 2020-01-31 11.00 - 12.00

Location: Kräftriket, house 5, room 31

Lecturer: Marko Kocic

Abstract

This paper aims to present the spectral theorem for normal operators and then describe the bilateral shift operator on a sequence space using the spectral theorem. To do so, the notion of Hilbert spaces needs to be defined first, and then we study bounded operators on a Hilbert space. The structures of bounded operators which are presented are the adjoint, the inverse, and the spectrum of bounded operators. Further the spectral theorem for self-adjoint operators is presented, which then gets extended to the spectral theorem for normal operators. Finally we apply the spectral theorem for normal operators to the bilateral shift operator.

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Belongs to: Department of Mathematics
Last changed: Jan 24, 2020