# (${\tilde{\varphi}}$, ${\tilde{\psi}}$)-AMENABILITY OF L1(G)

• Ghorbani, Zahra (Department of Mathematics, Jahrom University)
• Accepted : 2019.01.21
• Published : 2019.09.25
• 79 19

#### Abstract

In this paper we introduce and study the concept of of (${\varphi}$, ${\psi}$)-am-enability of a locally compact group G, where ${\varphi}$ is a continuous homomorphism on G and ${\psi}:G{\rightarrow}{\mathbb{C}}$ multiplicative linear function. We prove that if the group algebra $L^1$ (G) is (${\tilde{\varphi}}$, ${\tilde{\psi}}$)-amenable then G is (${\varphi}$, ${\psi}$)-amenable, where ${\tilde{\varphi}}$ is the extension of ${\varphi}$ to M(G). In the case where ${\varphi}$ is an isomorphism on G it is shown that the converse is also valid.

#### Keywords

Banach algebra;(${\varphi}$, ${\psi}$)- amenable

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