Amenability properties of certain Banach algebras of operators on Banach spaces
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http://id.loc.gov/authorities/names/n79058482
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Doctoral
Degree
Doctor of Philosophy
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Department of Mathematical and Statistical Sciences
Specialization
Mathematics
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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).
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http://purl.org/coar/resource_type/c_46ec
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This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. 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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en