Glasnik Matematicki, Vol. 53, No. 1 (2018), 187-203.

ON APPROXIMATE LEFT φ-BIPROJECTIVE BANACH ALGEBRAS

Amir Sahami and Abdolrasoul Pourabbas

Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516 Ilam, Iran
e-mail: a.sahami@ilam.ac.ir

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


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 l1(S) is approximate left character biprojective if and only if l1(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.

2010 Mathematics Subject Classification.   46M10, 43A07, 43A20.

Key words and phrases.   Approximate left φ-biprojectivity, left φ-amenability, Segal algebra, semigroup algebra, measure algebra.


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DOI: 10.3336/gm.53.1.13


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