In this paper, the notion of approximate \(\varphi\)-inner amenability for a Banach algebra A, where \(\varphi :A\rightarrow {\mathbb {C}}\) is a character, is defined and studied. Some hereditary properties of this new notion and its relation with other concepts of amenability are also given. As an application, the structure of \(\theta\)-Lau product algebras and upper triangular algebras are investigated.

中文翻译：

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关于近似 $$\varphi$$ φ -Inner Amenable Banach 代数

在本文中，定义和研究了 Banach 代数A的近似\(\varphi\) -inner amenability的概念，其中\(\varphi :A\rightarrow {\mathbb {C}}\)是一个字符。还给出了这一新概念的一些遗传特性及其与其他顺从性概念的关系。作为应用，研究了\(\theta\) -Lau积代数和上三角代数的结构。