Cyclicity of bounded linear operators on separable banach spaces and closed subspaces

The main focus of this thesis is to study some properties of diskcyclic operators. The similarities and differences between diskcyclic operators and the concepts of cyclicity are investigated. New classes of operators on the direct sum of Banach spaces, namely k-bitransitive, k-diskcyclic and k-comp...

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Main Author:	Muhemed Said, Nareen Sabih
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Linear operators
Online Access:	http://psasir.upm.edu.my/id/eprint/75481/1/FS%202016%2021%20-%20IR.pdf
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id	my-upm-ir.75481
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spelling	my-upm-ir.754812019-10-18T07:58:03Z Cyclicity of bounded linear operators on separable banach spaces and closed subspaces 2016-03 Muhemed Said, Nareen Sabih The main focus of this thesis is to study some properties of diskcyclic operators. The similarities and differences between diskcyclic operators and the concepts of cyclicity are investigated. New classes of operators on the direct sum of Banach spaces, namely k-bitransitive, k-diskcyclic and k-compound operators, are defined to study the direct sum of diskcyclic operators. A weaker property than chaotic operators, namely semi chaotic operators, is defined and studied to show that a chaos for linear operators exists on finite dimensions. Diskcyclicity concept is extended to closed subspaces of Banach spaces, and such a concept is called a subspace-diskcyclic operator. The similarities and differences between subspace-diskcyclicity and the subspace-cyclicity are investigated. Finally, some properties of hypercyclic operators are extended to subspace-hypercyclic operators to solve some open problems in the literature. This study shows that diskcyclic, semi chaotic and subspace-diskcyclic operators have some properties that are not shared with the existing concepts of cyclicity of operators. Linear operators 2016-03 Thesis http://psasir.upm.edu.my/id/eprint/75481/ http://psasir.upm.edu.my/id/eprint/75481/1/FS%202016%2021%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Linear operators
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Linear operators
spellingShingle	Linear operators Muhemed Said, Nareen Sabih Cyclicity of bounded linear operators on separable banach spaces and closed subspaces
description	The main focus of this thesis is to study some properties of diskcyclic operators. The similarities and differences between diskcyclic operators and the concepts of cyclicity are investigated. New classes of operators on the direct sum of Banach spaces, namely k-bitransitive, k-diskcyclic and k-compound operators, are defined to study the direct sum of diskcyclic operators. A weaker property than chaotic operators, namely semi chaotic operators, is defined and studied to show that a chaos for linear operators exists on finite dimensions. Diskcyclicity concept is extended to closed subspaces of Banach spaces, and such a concept is called a subspace-diskcyclic operator. The similarities and differences between subspace-diskcyclicity and the subspace-cyclicity are investigated. Finally, some properties of hypercyclic operators are extended to subspace-hypercyclic operators to solve some open problems in the literature. This study shows that diskcyclic, semi chaotic and subspace-diskcyclic operators have some properties that are not shared with the existing concepts of cyclicity of operators.
format	Thesis
qualification_level	Doctorate
author	Muhemed Said, Nareen Sabih
author_facet	Muhemed Said, Nareen Sabih
author_sort	Muhemed Said, Nareen Sabih
title	Cyclicity of bounded linear operators on separable banach spaces and closed subspaces
title_short	Cyclicity of bounded linear operators on separable banach spaces and closed subspaces
title_full	Cyclicity of bounded linear operators on separable banach spaces and closed subspaces
title_fullStr	Cyclicity of bounded linear operators on separable banach spaces and closed subspaces
title_full_unstemmed	Cyclicity of bounded linear operators on separable banach spaces and closed subspaces
title_sort	cyclicity of bounded linear operators on separable banach spaces and closed subspaces
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/75481/1/FS%202016%2021%20-%20IR.pdf
_version_	1747813056919896064

Cyclicity of bounded linear operators on separable banach spaces and closed subspaces

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