On σ-cyclic amenability for Banach algebras

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Ghaderi Eghbal; Nemati Mehdi; Naseri Saber

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Journal Paper

Paper Information

Journal: Mathematical Researches Year:2024 | Volume:10 | Issue:1 Page(s): 131-144

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Information Journal Paper

Title

On σ-cyclic amenability for Banach algebras

Author(s)

Ghaderi Eghbal | Nemati Mehdi | Naseri Saber | Issue Writer Certificate

Keywords

Banach algebras

trace extension property

σ-cyclic derivation

σ-cyclic amenability

unitization

θ-Lau product.

Abstract

Suppose that σ is homomorphism on Banach algebra A. Then in this paper we introduce and study the new two notions σ-cyclic derivation and σ-cyclic amenability for A. We investigate the relation between trace extension property and σ-cyclic amenability; indeed we show that the σ-cyclic amenability of AI implies that I has the trace extension property. Next, prove that the it’s converse can be true under the special conditions. One of the important result is that every σ-cyclic amenable is essential. Furthermore, for every closed two-sided ideal I of A, the relation between of σ-cyclic amenability of A and σ-cyclic amenability of AI has been studied. Also, we show that the σ-cyclic amenability of A and AI is equivalent. Finally, we study this notion on θ-Lau algebras and we investigate its relation with the similar concept on algebras A and B.

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