Seyyed Ali Kazemipour ¹, Mohammad Fozouni ²

Affiliations
1 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, IR
2 Department of Mathematics, Gonbad Kavous University, P. O. Box 163, Gonbad e-Kavous, Golestan, IR

Abstract

Let A be a Banach algebra and I be a non-zero closed two-sided ideal of A. We say that the Banach algebra A is I-quotient amenable if the quotient Banach algebra A / I is amenable. In this paper we study this notion and give a sufficient condition for I-quotient amenability. Also, we provide a characterization of I-quotient amenability whenever I has a bounded approximate identity. We prove that this notion may be coincide with amenability, then apply this result to give a new characterization for amenability of C *-algebras. Finally, we give some results over the Fourier algebra

Keywords

Amenability, C*-Algebra, Fourier Algebra, Quotient Algebra

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Seyyed Ali Kazemipour ¹, Amin Mahmoodi ¹

Affiliations
1 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, IR

Abstract

Suppose A is a presumably if intransitive commutative Banach algebra in its second dual A**. The paper studied several weaker definitions on amenability, Connes amenability including quotient pointwise amenability and approximate Connes amenability. Furthermore, the relations between them were discussed.

Keywords

Amenability, Connes Amenability, Pointwise Amenability, Quotient Banach Algebras, w*-Approximately Connes Amenability

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