Date of Award
Mathematics and Statistics
Sangani Monfared, Mehdi (Economics, Mathematics, and Statistics)
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In this thesis, we survey the properties of character amenable Banach algebras. Character amenability is a cohomological property weaker than the classical amenability introduced by B.E. Johnson. We give characterization of character amenability in terms of bounded approximate identities and certain topologically invariant elements of the second dual. In addition, we obtain equivalent characterizations of character amenability of Banach algebras in terms of variances of the approximate diagonal and the virtual diagonal. We show that character amenability for either the group algebra L1 (G) or the Herz-Figa-Talamanca algebra Ap (G) is equivalent to the amenability of the underlying group G. We also discuss hereditary properties of character amenability. In the case of uniform algebras we obtain complete characterization of character amenability in term of the Choquet boundary of the underlying space. In addition, we discuss character amenable version of the reduction of dimension formula and splitting properties of modules over character amenable Banach algebras.
Zhang, Jiaxin, "character amenable Banach algebras" (2012). Electronic Theses and Dissertations. 354.