Volume : 2, Issue : 5, May - 2013

SOME CHARACTERISTICS OF DERIVATIONS ON ??BANACH ALGEBRAS

Dr. Nilakshi Goswami

Abstract :

In this paper, we establish a correspondence between derivations on a ?–Banach algea and derivations on its right (and left) operator Banach algeas. Let M be a ?–Banach algea and R and L be respectively the right and left operator Banach algeas of M. We have shown that for a given derivation D on M, there exists a derivation on R, and also on L. Different properties of this derivation are discussed here. The converse of this result is also established for the ?–Banach algea M satisfying some specific conditions. Finally, we construct a derivation D? for the projective tensor product R??L and investigate some interesting properties of this derivation