Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. John Petrovic

Second Advisor

Dr. Yuri Ledyaev

Third Advisor

Dr. Jim Zhu

Fourth Advisor

Dr. Animikh Biswas


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

Included in

Algebra Commons