Daniel S. Sievewright
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Doctoral Dissertation Announcement
Candidate: Daniel S. Sievewright
Degree of:
Doctor of Philosophy
Department: Mathematics
Title: Weighted Shifts of Finite Multiplicity
Committee:
Dr. John Petrovic, Chair
Dr. Yuri Ledyaev
Dr. Jim Zhu
Dr. Animikh Biswas
Date: Friday, March 26, 2013 4:00 p.m. to 6:00 p.m.
6625 Everett Tower
Abstract:
We will discuss the structure of weighted shift operators on a separable, infinite dimensional, complex Hilbert space. A weighted shift is said to have multiplicity n when all the weights are n x n matrices. To study these weighted shifts, we will investigate which operators can belong to the Deddens algebras and spectral radius algebras, which can be quite large. This will lead to the necessary and sufficient conditions for these algebras to have a nontrivial invariant subspace.