Permanence of invariant subspaces under functional calculus and related topics

Author

Gabriel Titu Prǎjiturǎ

Date of Award

8-1999

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

John B. Conway

Committee Members

Michael Guidry, Stefan Richter, Carl Sundberg

Abstract

In this study several similarity-invariant classes of operators on a complex separable Hilbert space are considered. All these classes are defined in terms of an operator and its square having the same properties(generating the same algebras, having the same invariant subspaces or the same commutant). The interiors and some of the closures of these classes(in the norm topology) are characterized in terms of the various parts of the spectrum. Certain new techniques to approach non commutative approximation problems are developed.

Recommended Citation

Prǎjiturǎ, Gabriel Titu, "Permanence of invariant subspaces under functional calculus and related topics. " PhD diss., University of Tennessee, 1999.
https://trace.tennessee.edu/utk_graddiss/8904