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
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.