International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 359-368
-Derivations and their norm in projective tensor products of -Banach algebras
Department of Mathematics, Gauhati University, Guwahati 781 014, Assam, India
Received 16 April 1996; Revised 10 December 1996
Copyright © 1998 T. K. Dutta et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let and be Gamma-Banach algebras over the fields and
to a field
which possesses a real valued valuation, and , their projective tensor product.
It is shown that if
are - derivation and - derivation on and respectively and
, is an arbitrary element of , then there exists an - derivation
satisfying the relation
and possessing many enlightening properties. The converse is also true under a certain restriction.
Furthermore, the validity of the results
are fruitfully investigated.