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mmr 2021, 7(1): 101-110 |
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Sahami A, Rostami M, Essmaili M, Rahmani A. Biflatness of Abstract Segal Algebras Based on Characters. mmr 2021; 7 (1) :101-110
URL: http://mmr.khu.ac.ir/article-1-3056-en.html
URL: http://mmr.khu.ac.ir/article-1-3056-en.html
1- Ilam University
2- Amirkabir University ,mross@aut.ac.ir
3- Kharazmi University
4- Kurdistan University
2- Amirkabir University ,
3- Kharazmi University
4- Kurdistan University
Abstract: (2837 Views)
In this paper, we investigate and study the notion of left 
-biflatness of abstract Segal algebras, where is a character on Banach algebra. Precisely, we give a necessary and sufficient condition for left -biflatness of abstract Segal algebras equipped with a left approximate identity. As an application, we show that if 
is a Segal algebra on the locally group 
and 
is a character, then is left 
-biflat if and only if is amenable. Indeed, this is a generalization of [4, Theorem 3.4]. Moreover, we study the relationship between left -biflatness and inner -amenability and show that if the Banach algebra 
is inner -amenable, then the notions of left -biflatness and left -amenability are equivalent../files/site1/files/71/10.pdf
-biflatness of abstract Segal algebras, where is a character on Banach algebra. Precisely, we give a necessary and sufficient condition for left -biflatness of abstract Segal algebras equipped with a left approximate identity. As an application, we show that if is a Segal algebra on the locally group and is a character, then is left -biflat if and only if is amenable. Indeed, this is a generalization of [4, Theorem 3.4]. Moreover, we study the relationship between left -biflatness and inner -amenability and show that if the Banach algebra is inner -amenable, then the notions of left -biflatness and left -amenability are equivalent../files/site1/files/71/10.pdf
Keywords: Abstract, Segal algebra, left 𝜙-biflat, left 𝜙-amenable, inner 𝜙-amenable
2010 Mathematics Subject Classification: 64M10, 43A07, 43A20.
Type of Study: Original Manuscript |
Subject:
alg
Received: 2020/03/3 | Revised: 2021/05/24 | Accepted: 2020/11/23 | Published: 2021/05/31 | ePublished: 2021/05/31
Received: 2020/03/3 | Revised: 2021/05/24 | Accepted: 2020/11/23 | Published: 2021/05/31 | ePublished: 2021/05/31
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