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Let (V,Γ) and (V′,Γ′) be Gamma-Banach algebras over the fields F1 and F2 isomorphicto 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 andu=∑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 relationD(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

international journal of mathematics and mathematical sciences

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\alpha$"><mml:mi>α</mml:mi></mml:math>-Derivations and their norm in projective tensor products of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\Gamma$"><mml:mi>Γ</mml:mi></mml:math>-Banach algebras

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