Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

MODULE EXTENSION OF DUAL BANACH ALGEBRAS

  • Gordji, Madjid Eshaghi (DEPARTMENT OF MATHEMATICS SEMNAN UNIVERSITY) ;
  • Habibian, Fereydoun (DEPARTMENT OF MATHEMATICS SCIENCE BUILDING ISFAHAN UNIVERSITY, DEPARTMENT OF MATHEMATICS SEMNAN UNIVERSITY) ;
  • Rejali, Ali (DEPARTMENT OF MATHEMATICS SCIENCE BUILDING ISFAHAN UNIVERSITY)
  • Received : 2008.12.08
  • Published : 2010.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

This work was intended as an attempt to introduce and investigate the Connes-amenability of module extension of dual Banach algebras. It is natural to try to study the $weak^*$-continuous derivations on the module extension of dual Banach algebras and also the weak Connes-amenability of such Banach algebras.

Keywords

Acknowledgement

Supported by : Semnan University

References

  1. A. Connes, Classification of injective factors. Cases $II_1,\;II_{\infty},\;III_{\lamda},\;{\lamda}\;{\neg}\;1$, Ann. of Math. (2) 104 (1976), no. 1, 73–115. https://doi.org/10.2307/1971057
  2. A. Connes, On the cohomology of operator algebras, J. Functional Analysis 28 (1978), no. 2, 248–253. https://doi.org/10.1016/0022-1236(78)90088-5
  3. H. G. Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs. New Series, 24. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 2000.
  4. M. Eshaghi Gordji, Left introverted subspaces of duals of Banach algebras and $weak^{\ast}$ - continuous derivations on dual Banach algebras, Submitted.
  5. U. Haagerup, All nuclear $C^{\ast}-algebras$ are amenable, Invent. Math. 74 (1983), no. 2, 305–319. https://doi.org/10.1007/BF01394319
  6. B. E. Johnson, Cohomology in Banach Algebras, Memoirs of the American Mathematical Society, No. 127. American Mathematical Society, Providence, R.I., 1972.
  7. B. E. Johnson, R. V. Kadison, and J. Ringrose, Cohomology of operator algebras. III. Reduction to normal cohomology, Bull. Soc. Math. France 100 (1972), 73–96.
  8. V. Runde, Amenability for dual Banach algebras, Studia Math. 148 (2001), no. 1, 47–66. https://doi.org/10.4064/sm148-1-5
  9. V. Runde, Lectures on Amenability, Springer-Verlage, Berlin, Hedinberg, New York, 2002.
  10. W. Rudin, Functional Analysis: second edition, Mcgraw-Hill, 1991.
  11. S.Wassermann, On tensor products of certain group $C^{\ast}-algebras$, J. Functional Analysis 23 (1976), no. 3, 239–254. https://doi.org/10.1016/0022-1236(76)90050-1
  12. Y. Zhang, Weak amenability of module extensions of Banach algebras, Trans. Amer. Math. Soc. 354 (2002), no. 10, 4131–4151. https://doi.org/10.1090/S0002-9947-02-03039-8

Cited by

  1. Arens regularity of module actions and weak amenability of Banach algebras vol.71, pp.2, 2015, https://doi.org/10.1007/s10998-015-0103-2