MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS
Publish place: Journal of Mahani Mathematical Research، Vol: 2، Issue: 1
Publish Year: 1392
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_KJMMRC-2-1_004
تاریخ نمایه سازی: 5 خرداد 1398
Abstract:
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 $A_2^*$
Keywords:
Generalized amenable Banach algebra , Generalized rst cohomology group , Module generalized derivation , Triangular Banach algebra
Authors
MAYSAM MOSADEQ
DEPARTMENT OF MATHEMATICS, BEHBAHAN BRANCH, ISLAMIC AZAD UNIVERSITY, BEHBAHAN, IRAN.
ALIREZA ARABPOUR
DEPARTMENT OF STATISTICS, SHAHID BAHONAR UNIVERSITY OF KERMAN, IRAN.
MASHALLAH MASHINCHI
DEPARTMENT OF STATISTICS, SHAHID BAHONAR UNIVERSITY OF KERMAN, IRAN.