On the structure of Banach algebras associated with automorphisms

2002/09/04 by А. В. Лебедев, A. Lebedev, Lebedev, A.
Mathematics · #16W20 #46H15 #46H20 #47D30 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:16W20 #msc:46H15 #msc:46H20 #msc:47D30

paper · pdf · doi:10.48550/arxiv.math/0209040

34 pages

arxiv created 2002/09/04 · openalex publication_date 2002/09/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_{gg ∈ 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.

Related

• On the structure of Banach algebras associated with automorphisms. 2. Operators with measurable coefficients
• Isometries between groups of invertible elements in Banach algebras
• An algebraic property of an isometry between the groups of invertible elements in Banach algebras
• Linear extensions of isometries between groups of invertible elements in Banach algebras
• Self-induced Banach algebras