English

On the structure of Banach algebras associated with automorphisms

Operator Algebras 2007-05-23 v1

Abstract

In the present paper we study the structure of a Banach algebra B(A, T_g) generated by a certain Banach algebra AA 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.

Keywords

Cite

@article{arxiv.math/0209040,
  title  = {On the structure of Banach algebras associated with automorphisms},
  author = {A. Lebedev},
  journal= {arXiv preprint arXiv:math/0209040},
  year   = {2007}
}

Comments

34 pages

R2 v1 2026-07-22T16:47:25.636Z