Date of Award
4-2013
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Dr. John Petrovic
Second Advisor
Dr. Yuri Ledyaev
Third Advisor
Dr. Jim Zhu
Fourth Advisor
Dr. Animikh Biswas
Keywords
wieghted shifts, Deddens algebras, spectral radius algebra
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.
Access Setting
Dissertation-Open Access
Recommended Citation
Sievewright, Daniel S., "Weighted Shifts of Finite Multiplicity" (2013). Dissertations. 153.
https://scholarworks.wmich.edu/dissertations/153