Date of Award
Doctor of Philosophy
Dr. John Petrovic
Dr. Yuri Ledyaev
Dr. Jim Zhu
Dr. Animikh Biswas
wieghted shifts, Deddens algebras, spectral radius algebra
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.
Sievewright, Daniel S., "Weighted Shifts of Finite Multiplicity" (2013). Dissertations. 153.