标题：<mml:math alttext="$\alpha$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-Derivations and their norm in projective tensor products of <mml:math alttext="$\Gamma$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Γ</mml:mi></mml:math>-Banach algebras
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1998
卷号：21
DOI：10.1155/S0161171298000490
出版社：Hindawi Publishing Corporation
摘要：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=∑1x1⊗y1, is an arbitrary element of (V,Γ)⊗p(V′,Γ′), then there exists an α⊗α′- derivation
D on
(V,Γ)⊗p(V′,Γ′) satisfying the relation
D(u)=∑1[(D1x1)⊗y1
