Topics in the notion of operator amenability and its generalizations with application in Fourier algebras
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Date
2019-01-21
Authors
makareh shireh, miad
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Abstract
The operator algebraists have for a long time realized the significance of studying matrices
of elements of an operator algebra in order for obtaining results about the algebra. This
lead Z. J. Ruan, D. Blecher and others to introduce the notion of an abstract operator space
in late 1980’s. Ruan, furthermore, introduced the notion of completely contractive Banach
algebras and operator-space amenability for such algebras. He showed that the Fourier
algebra A(G) of a locally compact group G is operator-space amenable if and only if the
group G is amenable.
In this thesis we investigate further the notion of operator-space amenability and its approximate versions. In particular for the Fourier algebras. We also prove results on perturbation
theory of these notions.
Furthermore we study the question of when A⊗ˆB ( or A⊗γ B) is (approximately) operatorspace (or weakly) amenable what conclusions can one derive about the components.
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Keywords
Operator amenability, Fourier algebras