In recent work of the authors the notion of a derivation being approximately semi-inner arose as a tool for investigating (approximate) amenability questions for Banach algebras. Here we investigate this property in its own right, together with the consequent one of approximately semi-amenability. Under certain hypotheses regarding approximate identities this new notion is the same as approximate amenability, but more generally it covers some important classes of algebras which are not approximately amenable, in particular Segal algebras on amenable SIN-groups.

中文翻译：

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Banach 代数的近似半顺应性

在作者最近的工作中，近似半内推导的概念作为研究巴拿赫代数的（近似）顺应性问题的工具而出现。在这里，我们研究了这个属性本身，以及随之而来的近似半适应性的属性。在关于近似恒等式的某些假设下，这个新概念与近似服从性相同，但更一般地说，它涵盖了一些不是近似服从的重要代数类别，特别是适用于 SIN 群的 Segal 代数。