Amenability and weak$^*$-Continuous Derivations

Document Type : Original Article

Author

Department of Technology and Engineering, East of Guilan, University of Guilan, P.O. Box 44891-63157, Rudsar, Iran

Abstract

Generalizing the notion of character amenability for Banach algebras, we study the concept of $\varphi$-Connes amenability of a dual Banach algebra $\mathcal{A}$ with predual $\mathcal{A}_*$, where $\varphi$ is a homomorphism from $\mathcal{A}$ onto $\Bbb C$ that lies in $\mathcal{A}_*$. Also, we study $\Phi$-Connes amenability of $l^1$-Munn algebra $\mathcal{LM}(\mathcal{A}, P, m, n)$ that $\Phi$ is a character on $\mathcal{LM}(\mathcal{A}, P, m, n)$, $P$ is a sandavic matrix and $m,n\in \mathbb{N}$.  We show $\Phi$-Connes amenability  of $\mathcal{LM}(\mathcal{A}, P, m, n)$ is equivalent to $\phi$-Connes amenablity of $\mathcal{A}$ where $\phi$ is the unique character on $\mathcal{A}$ associated to $\Phi$. We discuss some hereditary properties of $\varphi$-Connes amenability. In fact, the investigation of  the hereditary properties of Connes amenability of projective tensor product of two  Banach algebras and the studying of the projectors on operator Banach algebras are the aims of  this paper.

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References

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Measure Algebras and Applications
Volume 2, Issue 2 - Serial Number 3
December 2024
Pages 82-93

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History

  • Receive Date: 05 August 2024
  • Revise Date: 01 November 2024
  • Accept Date: 08 November 2024

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