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GENERALIZED NOTION OF WEAK MODULE AMENABILITY

Year 2014, Volume: 43 Issue: 1, 85 - 95, 01.01.2014

Abstract

In the present paper, we introduce a new notion of weak moduleamenability for Banach algebras which is related to module homomorphisms. Among other results, we investigate the relationship betweenthis concept for a Banach algebraA which is a Banach A-bimodule withcompatible actions, and the quotient Banach algebraA/J where J isthe closed ideal ofA generated by elements of the form (a·α)b−a(α·b)for a ∈A and α ∈ A. We then study this concept for an inversesemigroup S, where some examples on(S) and C∗ (S) are given.

References

  • M. Amini, Module amenability for semigroup algebras, Semigroup Forum 69, 243–254, 2004. M. Amini and A. Bodaghi, Module amenability and weak module amenability for second dual of Banach algeras, Chamchuri J. Math. 2, No. 1, 57–71, 2010.
  • M. Amini, A. Bodaghi and D. Ebrahimi Bagha, Module amenability of the second dual and module topological center of semigroup algebras, Semigroup Forum 80, 302–312, 2010.
  • M. Amini and D. Ebrahimi Bagha, Weak Module Amenability for semigroup algebras, Semigroup Forum 71, 18–26, 2005.
  • 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), 359–377, 1987.
  • A. Bodaghi, Semigroup algebras and their weak module amenability, J. Appl. Func. Anal. 7, No. 4, 332–338, 2012.
  • A. Bodaghi, Module (ϕ, ψ)-amenability of Banach algeras, Arch. Math (Brno) 46, No. 4, 227–235, 2010.
  • A. Bodaghi, M. Eshaghi Gordji and A. R. Medghalchi, A generalization of the weak amenability of Banach algebras, Banach J. Math. Anal. 3, No. 1, 131–142, 2009.
  • S. Bowling and J. Duncan, Order cohomology of Banach semigroup algebras, Semigroup Forum 56, 130–145, 1998.
  • H. G. Dales, Banach Algebras and Automatic Continuity, Oxford University Press, Oxford, 2000.
  • R. S. Doran and J. Wichmann, Approximate Identities and Factorization in Banch Modules, Lecture Notes in Mathematics 768, Springer, Berlin, 1979.
  • J. Duncan and I. Namioka, Amenability of inverse semigroups and their semigroup algebras, Proc. Roy. Soc. Edinburgh 80A, 309-321, 1988.
  • J. Duncan and A. L. T. Paterson, C ∗ -algebras of inverse semigroups, Proc. Roy. Soc. Edinburgh Soc. 28, 41–58, 1985.
  • M. Eshaghi Gordji and A. Jabbari, Generalization of weak amenability of group algebras, preprint. U. Haagerup, All nuclear C ∗ -algebras are amenable, Invent. Math. 74, 305–319, 1983.
  • U. Haagerup and N. J. Laustsen, Weak amenability of C ∗ -algebras and theorem of Goldstien, In Banach algebra 97. 223–243. J. M. Howie, An Introduction to Semigroup Theory, Academic Press, London, 1976.
  • B. E. Johnson, Cohomology in Banach Algebras, Memoirs Amer. Math. Soc. 127, American Math. Soc., Providence, 1972.
  • B. E. Johnson, Derivation from L 1 (G) into L 1 (G) and L ∞ (G), Lecture Note in Math. 1359, 191–198, 1988.
  • B. E. Johnson, Weak amenability of group Algebras, Bull. London Math. Soc. 23 (3), 281– 284, 1991.
  • M. S. Moslehian and A. N. Motlagh, Some notes on (σ, τ )-amenability of Banach algebras , Stud. Univ. Babes-Bolyai. Math. 53, No. 3, 57–68, 2008.
  • A. L. T. Paterson, Amenability, American Math. Soc., Providence, Rhode Island, 1988.
  • H. Pourmahmood-Aghababa, (Super )Module amenability, module topological center and semigroup algebras, Semigroup Forum. 81, 344–356, 2010.
  • R. Rezavand, M. Amini, M. H. Sattari and D. Ebrahimi Bagha, Module Arens regularity for semigroup algebras, Semigroup Forum. 77, 300–305, 2008.

GENERALIZED NOTION OF WEAK MODULE AMENABILITY

Year 2014, Volume: 43 Issue: 1, 85 - 95, 01.01.2014

Abstract

-

References

  • M. Amini, Module amenability for semigroup algebras, Semigroup Forum 69, 243–254, 2004. M. Amini and A. Bodaghi, Module amenability and weak module amenability for second dual of Banach algeras, Chamchuri J. Math. 2, No. 1, 57–71, 2010.
  • M. Amini, A. Bodaghi and D. Ebrahimi Bagha, Module amenability of the second dual and module topological center of semigroup algebras, Semigroup Forum 80, 302–312, 2010.
  • M. Amini and D. Ebrahimi Bagha, Weak Module Amenability for semigroup algebras, Semigroup Forum 71, 18–26, 2005.
  • 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), 359–377, 1987.
  • A. Bodaghi, Semigroup algebras and their weak module amenability, J. Appl. Func. Anal. 7, No. 4, 332–338, 2012.
  • A. Bodaghi, Module (ϕ, ψ)-amenability of Banach algeras, Arch. Math (Brno) 46, No. 4, 227–235, 2010.
  • A. Bodaghi, M. Eshaghi Gordji and A. R. Medghalchi, A generalization of the weak amenability of Banach algebras, Banach J. Math. Anal. 3, No. 1, 131–142, 2009.
  • S. Bowling and J. Duncan, Order cohomology of Banach semigroup algebras, Semigroup Forum 56, 130–145, 1998.
  • H. G. Dales, Banach Algebras and Automatic Continuity, Oxford University Press, Oxford, 2000.
  • R. S. Doran and J. Wichmann, Approximate Identities and Factorization in Banch Modules, Lecture Notes in Mathematics 768, Springer, Berlin, 1979.
  • J. Duncan and I. Namioka, Amenability of inverse semigroups and their semigroup algebras, Proc. Roy. Soc. Edinburgh 80A, 309-321, 1988.
  • J. Duncan and A. L. T. Paterson, C ∗ -algebras of inverse semigroups, Proc. Roy. Soc. Edinburgh Soc. 28, 41–58, 1985.
  • M. Eshaghi Gordji and A. Jabbari, Generalization of weak amenability of group algebras, preprint. U. Haagerup, All nuclear C ∗ -algebras are amenable, Invent. Math. 74, 305–319, 1983.
  • U. Haagerup and N. J. Laustsen, Weak amenability of C ∗ -algebras and theorem of Goldstien, In Banach algebra 97. 223–243. J. M. Howie, An Introduction to Semigroup Theory, Academic Press, London, 1976.
  • B. E. Johnson, Cohomology in Banach Algebras, Memoirs Amer. Math. Soc. 127, American Math. Soc., Providence, 1972.
  • B. E. Johnson, Derivation from L 1 (G) into L 1 (G) and L ∞ (G), Lecture Note in Math. 1359, 191–198, 1988.
  • B. E. Johnson, Weak amenability of group Algebras, Bull. London Math. Soc. 23 (3), 281– 284, 1991.
  • M. S. Moslehian and A. N. Motlagh, Some notes on (σ, τ )-amenability of Banach algebras , Stud. Univ. Babes-Bolyai. Math. 53, No. 3, 57–68, 2008.
  • A. L. T. Paterson, Amenability, American Math. Soc., Providence, Rhode Island, 1988.
  • H. Pourmahmood-Aghababa, (Super )Module amenability, module topological center and semigroup algebras, Semigroup Forum. 81, 344–356, 2010.
  • R. Rezavand, M. Amini, M. H. Sattari and D. Ebrahimi Bagha, Module Arens regularity for semigroup algebras, Semigroup Forum. 77, 300–305, 2008.
There are 21 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Abasalt Bodaghi This is me

Publication Date January 1, 2014
Published in Issue Year 2014 Volume: 43 Issue: 1

Cite

APA Bodaghi, A. (2014). GENERALIZED NOTION OF WEAK MODULE AMENABILITY. Hacettepe Journal of Mathematics and Statistics, 43(1), 85-95.
AMA Bodaghi A. GENERALIZED NOTION OF WEAK MODULE AMENABILITY. Hacettepe Journal of Mathematics and Statistics. January 2014;43(1):85-95.
Chicago Bodaghi, Abasalt. “GENERALIZED NOTION OF WEAK MODULE AMENABILITY”. Hacettepe Journal of Mathematics and Statistics 43, no. 1 (January 2014): 85-95.
EndNote Bodaghi A (January 1, 2014) GENERALIZED NOTION OF WEAK MODULE AMENABILITY. Hacettepe Journal of Mathematics and Statistics 43 1 85–95.
IEEE A. Bodaghi, “GENERALIZED NOTION OF WEAK MODULE AMENABILITY”, Hacettepe Journal of Mathematics and Statistics, vol. 43, no. 1, pp. 85–95, 2014.
ISNAD Bodaghi, Abasalt. “GENERALIZED NOTION OF WEAK MODULE AMENABILITY”. Hacettepe Journal of Mathematics and Statistics 43/1 (January 2014), 85-95.
JAMA Bodaghi A. GENERALIZED NOTION OF WEAK MODULE AMENABILITY. Hacettepe Journal of Mathematics and Statistics. 2014;43:85–95.
MLA Bodaghi, Abasalt. “GENERALIZED NOTION OF WEAK MODULE AMENABILITY”. Hacettepe Journal of Mathematics and Statistics, vol. 43, no. 1, 2014, pp. 85-95.
Vancouver Bodaghi A. GENERALIZED NOTION OF WEAK MODULE AMENABILITY. Hacettepe Journal of Mathematics and Statistics. 2014;43(1):85-9.