2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69393A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a fertile framework for developing homological aspects of unital Banach algebras. Elementary results with applictions to computations of the bounded Hochschild cohomology groups H^1(A,A^*) with emphasis on A=A(X), the approximable operators on a Banach space X, are given.14 pages, submitted to conference proceedingsFunctional AnalysisOperator Algebras47L10 (Primary); 46M18, 16D90 (Secondary)text