DOI QR코드

DOI QR Code

MODULE AMENABILITY OF MODULE LAU PRODUCT OF BANACH ALGEBRAS

  • Received : 2019.12.04
  • Accepted : 2020.08.11
  • Published : 2020.09.25

Abstract

Let A, B, 𝔘 be Banach algebras and B be a Banach 𝔘-bimodule also A be a Banach B-𝔘-module. In this paper we study the relation between module amenability, weak module amenability and module approximate amenability of module Lau product A × α B and that of Banach algebras A, B.

Keywords

References

  1. M. Amini,Module amenability for semigroup algebras, Semigroup Forum, 69(2004), 243-254. https://doi.org/10.1007/s00233-004-0107-3
  2. M. Amini and A. Bodaghi, module amenability and weak module amenability for second dual of Banach algebras, Chamchuri Journal of Math. (2010), 57-71.
  3. M. Amini and D. Ebrahimi Bagha, Weak module amenability for semigroup algebras, Semigroup Forum, 71 (2005), 18-26. https://doi.org/10.1007/s00233-004-0166-5
  4. W.G. Bade, P.C. Curtis and H.G. Dales, Amenability and weak amenability for Beurling and Lipschits algebra, Proc. London Math. Soc., 55(3)(1987), 359-377.
  5. S.J. Bhatt and P.A. Dabhi, Arens regularity and amenability of Lau product of Banach algebras defined by a Banach algebra morphism, Bull. Aust. Math. Soc., 87 (2013), 195-206. https://doi.org/10.1017/S000497271200055X
  6. A. Bodaghi and M. Amini,Module character amenability of Banach algebras, Arch. Math. (Basel), 99 (2012), 353-365. https://doi.org/10.1007/s00013-012-0430-y
  7. A. Bodaghi, M. Amini and R. Babaee,Module derivations into iterated duals of Banach algebras, Proc. Rom. Aca. Series A, 12 (4) (2011), 227-284.
  8. A. Bodaghi, M. Amini and A. Jabbari, Permanent weak module amenability of semigroup algebras, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.). Tomul LXIII (2017), 287-296.
  9. A.Bodaghi and A.Jabbari, n-weak module amenability of triangular Banach algebras, Math. Slovaca, 65(2015), 645-666. https://doi.org/10.1515/ms-2015-0045
  10. P.A. Dabhi, A. Jabbari and K.H. Azar, Some notes on amenability and weak amenability of Lau product of Banach algebras defined by a Banach algebra morphism, Acta Math. Sin. (Engl. Ser.), 31(2015), 1461-1474. https://doi.org/10.1007/s10114-015-4429-8
  11. H. Javansiri and M. Nemati, On a certain product of Banach algebras and some of its properties, Proc. Rom. Acad. Ser. A, 15 (2014), 219-227.
  12. B.E. Johnson,Weak amenability of group Algebras, Bull. London Math. Soc., 23 (1991), 281-284. https://doi.org/10.1112/blms/23.3.281
  13. B.E. Johnson, Derivation from $L^1(G)$ into $L^1(G)$ and $L^{\infty}(G)$, Lecture Note in Math., (1988), 191-198 .
  14. B.E. Johnson, Cohomology in Banach algebras, Memoirs Amer.Math.Soc., 127, 1972.
  15. H. Pourmahmood-Aghababa and A.Bodaghi, Module approximate amenability of Banach algebras, Bulletin of Iranian Mathematical Soc., 39 (2013), 1137-1158.