MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS
نویسنده
چکیده مقاله:
Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations from the triangular Banach algebraof the form $mathcal{T} :=left(begin{array}{lc} A_1 &X 0 & A_2end{array}right)$ into the associated triangular $mathcal{T}$- bimodule $mathcal{T}^*$ of theform $mathcal{T}^*:=left(begin{array}{lc} A_1^* &X^* 0 & A_2^*end{array}right)$. In particular, we show that the so-called generalized first cohomology group from $mathcal{T}$ to $mathcal{T}^*$ is isomorphic to the directed sum of the generalized first cohomology group from $A_1$ to $A^*_1$ and the generalized first cohomology group from $A_2$ to $A_2^*$
منابع مشابه
module generalized derivations on triangulaur banach algebras
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عنوان ژورنال
دوره 2 شماره 1
صفحات 43- 52
تاریخ انتشار 2014-01-26
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