On the structure of Banach algebras associated with automorphisms. 2. Operators with measurable coefficients

Details On the structure of Banach algebras associated with automorphisms. 2. Operators with measurable coefficients On the structure of Banach algebras associated with automorphisms. 2. Operators with measurable coefficients

2002-09-04

arxiv.org/abs/math/0209039v1

Mathematics

Operator Algebras

24 pages

Scientific paper

In the present paper we continue the study of 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 $A$, metrical 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 Lebesgue spaces.

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