On Bounded Operators on a Banach Space and Derivations on Projective Tensor Algebras

摘要

We consider a Banach space endowed with a shrinking basis. Then we describe the structure of derivations on the projective Banach algebra which are induced by bounded linear operators on . If the underlying space has no such basis our results are no longer applicable. However, if is the space of absolutely convergent complex series we establish a relationship between bounded derivations on and bounded derivations on