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Permanent link (DOI): https://doi.org/10.7939/R3ZS2KT01

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Amenability properties of certain Banach algebras of operators on Banach spaces Open Access

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Other title
Subject/Keyword
Weak amenability
Banach algebras of operators
Amenability
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Aldabbas, Eman IA
Supervisor and department
Runde, Volker (Mathematical and Statistical Sciences)
Examining committee member and department
Lykova, Zinaida (School of Mathematics, Statistics and Physics)
Guay, Nicolas (Mathematical and Statistical Sciences)
Berger, Arno (Mathematical and Statistical Sciences)
Runde, Volker (Mathematical and Statistical Sciences)
Lau, Anthony (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2017-09-27T15:37:45Z
Graduation date
2017-11:Fall 2017
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
In this thesis, we prove the non-amenability of the Banach algebra B(E), the banach algebra of all operators on an infinite dimensional Banach space E, where, for p in the interval [1,infinity), E is an infinite dimensional Lp-space in the sense of Lindenstrauss and Pelczynski. In addition, we prove that SS(E), the Banach algebra of all strictly singular operators on E, is not weakly amenable if E=C[0,1] or E= Lp[0,1], where p is in the interval [1,infinity). Then, we generalize this last result to all infinite dimensional separable Lp-spaces E such that E is not isomorphic to lp for p in the interval (1,infinity).
Language
English
DOI
doi:10.7939/R3ZS2KT01
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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