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On the structure of Banach algebras associated with automorphisms

A. Lebedev
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Abstract

In the present paper we study the structure of a Banach algebra B(A, T_g) generated by a certain Banach algebra $A$ of operators acting in a Banach space D and a group {T_g}_{g \in G} of isometries of D such that T_g A T^{-1}_g = A. We investigate the interrelations between the existence of the expectation of B(A, T_g) onto A, topological freedom of the automorphisms of A induced by T_g and the dual action of the group G on B(A, T_g). The results obtained are applied to the description of the structure of Banach algebras generated by 'weighted composition operators' acting in various spaces.

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A. Lebedev. 2002-09-04. On the structure of Banach algebras associated with automorphisms. https://arxiv.org/abs/math/0209040

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