α-derivations and their norm in projective tensor products of Γ-banach algebras
Clicks: 172
ID: 173627
1998
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Abstract
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+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.
| Reference Key |
dutta1998international-derivations
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|---|---|
| Authors | ;T. K. Dutta;H. K. Nath;R. C. Kalita |
| Journal | structural engineering and mechanics |
| Year | 1998 |
| DOI |
10.1155/S0161171298000490
|
| URL | |
| Keywords |
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