Original scientific paper

https://doi.org/10.3336/gm.51.1.04

A characterization of biflatness of Segal algebras based on a character

Morteza Essmaili ; Department of Mathematics, Faculty of Mathematical and Computer Sciences, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran
Mehdi Rostami ; Faculty of Mathematical and Computer Science , Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran
Massoud Amini ; Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran

Abstract

Let A be a Banach algebra and φ be a character on A. In this paper, we give a necessary condition, called condition (W), for φ-biflatness of Banach algebra A as well as some hereditary properties. We also study the relation between left φ-amenability and condition (W). Moreover, we apply these results and characterize the φ-biflatness of abstract symmetric Segal algebras. In particular, we identify φ-biflatness of the Lebesgue-Fourier algebra A(G), where G is a unimodular locally compact group. These results describe a homological property for Segal algebras in the setting of biflatness based on character φ.

Keywords

phi-biflatness; phi-amenability; group algebras; abstract Segal algebras

Hrčak ID:

160102

URI

https://hrcak.srce.hr/160102

Publication date:

15.6.2016.

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