Approximate left $\phi$-biprojectivity of $\theta$-Lau product algebras

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran

2 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

3 Department of Mathematics, Farhangian University of Kermanshah, Kermanshah, Iran

4 Department of Mathematics, Faculty of Basic Sciences Ilam University P.O. Box 69315-516 Ilam, Iran

Abstract

We continue [8] and we discuss approximately left $\phi$-biprojectivity for $\theta$-Lau product algebras. We give some Banach algebras among the category of $\theta$-Lau product algebras which are not approximately left $\phi$-biprojective. In fact, some class of matrix algebras under the notion of approximate left $\phi$-biprojectivity is also discussed here.

Keywords

Main Subjects


  1. P. Aghababa, L. Y. Shi, and Y. J. Wu, Generalized notions of character amenability, Acta Math. Sin. (Engl. Ser.), 29 (2013), pp. 1329–1350.
  2. Askari-Sayah, A. Pourabbas, and A. Sahami, Johnson pseudo-contractibility and pseudo-amenability of θ-Lau product, Kragujevac J. Math., 44 (2020), pp. 593–601.
  3. Kaniuth, A. T. Lau, and J. Pym, On ϕ-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), pp. 85–96.
  4. T. M. Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math., 118 (1983), pp. 161–175.
  5. S. Monfared, On certain products of Banach algebras with applications to harmonic analysis, Studia Math., 178 (2007), pp. 277–294.
  6. Runde, Lectures on amenability, vol. 1774 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2002.
  7. Sahami, On biflatness and ϕ-biflatness of some Banach algebras, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 80 (2018), pp. 111–122.
  8. Sahami and A. Pourabbas, On approximate left ϕ-biprojective Banach algebras, Glas. Mat. Ser. III, 53(73) (2018), pp. 187–203.
  9. Zhang, Nilpotent ideals in a class of Banach algebras, Proc. Amer. Math. Soc., 127 (1999), pp. 3237–3242.