Original scientific paper

https://doi.org/10.3336/gm.53.1.13

On approximate left φ-biprojective Banach algebras

Amir Sahami orcid.org/0000-0003-0041-509X ; Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516 Ilam, Iran
Abdolrasoul Pourabbas ; Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran

Abstract

Let A be a Banach algebra. We introduce the notions of approximate left φ-biprojective and approximate left character biprojective Banach algebras, where φ is a non-zero multiplicative linear functional on A. We show that for a SIN group G, the Segal algebra S(G) is approximate left φ1-biprojective if and only if G is amenable, where φ1 is the augmentation character on S(G). Also we show that the measure algebra M(G) is approximate left character biprojective if and only if G is discrete and amenable. For a Clifford semigroup S, we show that \(l^1(S)\) is approximate left character biprojective if and only if \(l^1(S)\) is pseudo-amenable. We study the hereditary property of these notions. Finally we give some examples to show the differences of these notions and the classical ones.

Keywords

Approximate left φ-biprojectivity; left φ-amenability; Segal algebra; semigroup algebra; measure algebra

Hrčak ID:

201831

URI

https://hrcak.srce.hr/201831

Publication date:

20.6.2018.

Visits: 1.225 *