  A 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.
