2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64848In 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.24 pagesOperator Algebras47L30, 16W20, 46H15, 46H20text