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

Department of Mathematics, Faculty of Mathematical and Computer Sciences, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran
e-mail: m.essmaili@khu.ac.ir

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.


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DOI: 10.3336/gm.51.1.04


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