Addendum to “Amenability and weak amenability of second conjugate Banach algebras”,Proceedings of the American Mathematical Society

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Addendum to “Amenability and weak amenability of second conjugate Banach algebras”
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-06-30 , DOI: 10.1090/proc/15009
F. Ghahramani , R. J. Loy , G. A. Willis

Abstract:The purpose of this note is to show that if

is a Banach algebra with the continuous dual space $A^{*}$ and $D : A \rightarrow A^{*}$ is a weakly compact derivation, then $D^{**} : A^{**} \rightarrow A^{***}$ is also a derivation, where $A^{**}$ has the first (or second) Arens product and $A^{***}$ is viewed as the dual module of the Banach algebra $A^{**}.$

中文翻译：

“第二共轭Banach代数的可及性和弱可及性”的附录

摘要：本说明的目的是证明，如果

是具有连续对偶空间的Banach代数 $A ^ {*}$ 并且是弱紧致的导数，那么它也是一个推导，其中具有第一（或第二）Arens乘积并且被视为对偶Banach代数的模块 $D：一个\ rightarrow A ^ {*}$ $D ^ {**}：A ^ {**} \ rightarrow A ^ {***}$ $A ^ {**}$ $A ^ {***}$ $A ^ {**}。$

更新日期：2020-08-20

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