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Dissertation/Thesis Abstract

On Expansive Mappings and Non-hypercyclicity
by Sichel, Edward Simon, M.S., California State University, Fresno, 2019, 74; 27664289
Abstract (Summary)

We take a close look at the nature of expansive mappings on certain metric spaces (compact, totally bounded, and bounded), provide a finer classification for such mappings, and use them to characterize boundedness. We also furnish a simple straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator in a complex Hilbert space as well as of a certain collection of its exponentials and establish non-hypercyclicity for symmetric operators.

Indexing (document details)
Advisor: Markin, Marat V.
Commitee: Bishop, Michael, Kajetanowicz, Przemyslaw
School: California State University, Fresno
Department: Mathematics
School Location: United States -- California
Source: MAI 81/6(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Expansion, Functional analysis, Hypercyclicity, Metric space, Nonlinear functional analysis, Operator theory
Publication Number: 27664289
ISBN: 9781392773345
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