International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 359-368

α-Derivations and their norm in projective tensor products of Γ-Banach algebras

T. K. Dutta, H. K. Nath, and R. C. Kalita

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 (V,Γ) and (V,Γ) be Gamma-Banach algebras over the fields F1 and F2 isomorphic to a field F which possesses a real valued valuation, and (V,Γ)p(V,Γ), their projective tensor product. It is shown that if D1 and D2 are α - derivation and α - derivation on (V,Γ) and (V,Γ) respectively and u=1x1y1, is an arbitrary element of (V,Γ)p(V,Γ), then there exists an αα- derivation D on (V,Γ)p(V,Γ) satisfying the relation D(u)=1[(D1x1)y1+x1(D2y1)] and possessing many enlightening properties. The converse is also true under a certain restriction. Furthermore, the validity of the results D=D1+D2 and sp(D)=sp(D1)+sp(D2) are fruitfully investigated.