The geometry of the projective joint spectrum and the commutativity of self-adjoint operators

Author

Isaak Chagouel, University at Albany, State University of New YorkFollow

Date of Award

1-1-2014

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (vii, 59 pages)

Dissertation/Thesis Chair

Michael Stessin

Committee Members

Rongwei Yang, Kehe Zhu

Keywords

Complete Reducibility of the Characteristic Polynomial, Eigenvalues, Normal Matrices, Operator Theory, Projective Joint Spectrum, Self-Adjoint Operators, Selfadjoint operators, Linear operators, Operator theory, Spectral theory (Mathematics)

Subject Categories

Applied Mathematics | Mathematics | Physical Sciences and Mathematics

Abstract

The theory of single operators is by now a very mature subject, with the notion of spectrum playing a key role in the theory. However, multivariate operator theory is only in its very early stages of development. There is not even wide agreement about how "the joint spectrum" of an n-tuple A = (A₁, · · · , A_n) of bounded linear operators on the same Hilbert space H should be defined.

Recommended Citation

Chagouel, Isaak, "The geometry of the projective joint spectrum and the commutativity of self-adjoint operators" (2014). Legacy Theses & Dissertations (2009 - 2024). 1098.
https://scholarsarchive.library.albany.edu/legacy-etd/1098