Glasnik Matematicki, Vol. 51, No. 1 (2016), 45-58.

A CHARACTERIZATION OF BIFLATNESS OF SEGAL ALGEBRAS BASED ON A CHARACTER

Morteza Essmaili, Mehdi Rostami and Massoud Amini

Faculty of Mathematical and Computer Science , Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran
e-mail: mross@aut.ac.ir

Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran
e-mail: mamini@modares.ac.ir

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.

2010 Mathematics Subject Classification.   16E40, 43A20.

Key words and phrases.   φ-biflatness, φ-amenability, group algebras, abstract Segal algebras.

DOI: 10.3336/gm.51.1.04

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