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.
|Advisor:||Markin, Marat V.|
|Commitee:||Bishop, Michael, Kajetanowicz, Przemyslaw|
|School:||California State University, Fresno|
|School Location:||United States -- California|
|Source:||MAI 81/6(E), Masters Abstracts International|
|Keywords:||Expansion, Functional analysis, Hypercyclicity, Metric space, Nonlinear functional analysis, Operator theory|
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