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- W3140927352 abstract "A Banach algebra $mathfrak{A}$ has a generalized Matrix representation if there exist the algebras $A, B$, $(A,B)$-module $M$ and $(B,A)$-module $N$ such that $mathfrak{A}$ is isomorphic to the generalized matrix Banach algebra $Big[begin{array}{cc}A & M N & B%end{array}%Big]$.In this paper, the algebras with generalized matrix representation will be characterized. Then we show that there is a unital permanently weakly amenable Banach algebra $A$ without generalized matrix representation such that $H^1(A,A)={0}$.This implies that there is a unital Banach algebra $A$ without any triangular matrix representation such that $H^1(A,A)={0}$ and gives a negative answer to the open question of cite{D}." @default.
- W3140927352 created "2021-04-13" @default.
- W3140927352 creator A5073292392 @default.
- W3140927352 date "2020-11-01" @default.
- W3140927352 modified "2023-09-23" @default.
- W3140927352 title "The Banach algebras with generalized matrix representation" @default.
- W3140927352 doi "https://doi.org/10.22072/wala.2020.122402.1273" @default.
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