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Permanent link (DOI): https://doi.org/10.7939/R36395

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Irreducible Operators and Semigroups on Banach Lattices Open Access

Descriptions

Other title
Subject/Keyword
irreducible operators
irreducible semigroups
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Gao, Niushan
Supervisor and department
Litvak, Alexander (Math)
Troitsky, Vladimir (Math)
Examining committee member and department
Litvak, Alexander (Math)
Tcaciuc, Adi (Math)
Troitsky, Vladimir (Math)
Lau, Anthony (Math)
Drnovsek, Roman (Math)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2013-08-28T13:32:18Z
Graduation date
2013-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
In this thesis, I study irreducibility on Banach lattices. First, I study irreducible positive operators on Banach lattices. I develop a uniform approach to several comparison theorems of positive operators. I also use a comparison theorem to show that if one of the two semi-commuting positive operators is compact then their commutator is quasinilpotent. Second, I study irreducible semigroups of positive operators on arbitrary Banach lattices. An extension of Perron-Frobenius theory is established and applied to improve some classical results. Third, I study compact positive operators K with irreducible super right or left commutants (which are always semigroups). I prove that every operator semi-commuting with K commutes with K. I also prove that the restriction of K to its peripheral spectral subspace is a permutation.
Language
English
DOI
doi:10.7939/R36395
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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