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Ideal Module Amenability of Triangular Banach Algebras


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1 University of Birjand, Birjand, Iran, Islamic Republic of
     

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Let A and B be unital Banach algebras and M be an unital Banach A,B-module. In this paper we define the concept of the (n)-ideal module amenability of Banach algebras and investigate the relation between the (2n-1)-ideal module amenability of triangular Banach algebra Τ = [A M B] (as a Τ = {[α α] : α ∈u}-module) and (2n - 1)-ideal module amenability of A and B (as an u-module), where u is a (not necessarily unital) Banach algebra such that A, B and M are commutative Banach u-bimodules. Finally, in the case that A = B = M = l1(S) and u = l1(E), for unital and commutative inverse semigroup S with idempotent set E, we show that T as an u-module is (2n - 1)- ideal module amenable while is not module amenable.

Keywords

Ideal Module Amenability, Inverse Semigroup Algebras, Module Amenability, Triangular Banach Algebras.
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  • M. Amini, Module amenability for semigroup algebras, Semigroup Forum 69 (2004), 243–254.
  • M. Amini and B. E. Bagha, Weak Module amenability for semigroup algebras, Semigroup Forum 71 (2005) 18–26.
  • W. G. Bade, P. C. Curtis and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London. Math. Soc 3.2 (1987), 359–377.
  • A. Bodaghi, A. Jabbari, n-Weak Module Amenability of Triangular Banach algebras Math. Slovaca 65.3 (2015), 645–666.
  • B. E. Forrest and L. W. Marcoux, Weak Amenability of Triangular Banach algebras, Tranc. Amer. Math. Soc 345 (2002), 1435–1452.
  • M. E. Gordji and S. A. R. Hosseiniun, Ideal amenability of Banach algebras on locally compact groups, Proc. Indian Acad. Sc 115 (2005), No. 3, 319–325.
  • M. E. Gordjiand and T. Yazdanpanah, Derivations into duals of ideals of Banach algebras, Proc. Indian Acad. Sci 114(4) (2004), 399–408
  • B. E. Johnson, Cohomology in Banach algebras Memoirs Amer. Math. Soc 127 (1972), 96 pp.
  • B. E. Johnson and M.C. White, A non-weakly amenable augmentation ideal, To appear, (2003).
  • A. R. Pourabbas and E. Nasrabadi, Weak Module Amenability of Triangular Banach Algebras, Mathematica Slovaca. 61 (2011), 949–958.

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  • Ideal Module Amenability of Triangular Banach Algebras

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Authors

Ebrahim Nasrabadi
University of Birjand, Birjand, Iran, Islamic Republic of

Abstract


Let A and B be unital Banach algebras and M be an unital Banach A,B-module. In this paper we define the concept of the (n)-ideal module amenability of Banach algebras and investigate the relation between the (2n-1)-ideal module amenability of triangular Banach algebra Τ = [A M B] (as a Τ = {[α α] : α ∈u}-module) and (2n - 1)-ideal module amenability of A and B (as an u-module), where u is a (not necessarily unital) Banach algebra such that A, B and M are commutative Banach u-bimodules. Finally, in the case that A = B = M = l1(S) and u = l1(E), for unital and commutative inverse semigroup S with idempotent set E, we show that T as an u-module is (2n - 1)- ideal module amenable while is not module amenable.

Keywords


Ideal Module Amenability, Inverse Semigroup Algebras, Module Amenability, Triangular Banach Algebras.

References