Derivations into iterated duals of Banach algebras

H. Dales; F. Ghahramani; N. Grønbæek

Studia Mathematica (1998)

  • Volume: 128, Issue: 1, page 19-54
  • ISSN: 0039-3223

Abstract

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We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space A ( n ) is zero; i.e., ℋ 1 ( A , A ( n ) ) = 0 . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study group algebras, C*-algebras, Banach function algebras, and algebras of operators. Our results are summarized and some open questions are raised in the final section.

How to cite

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Dales, H., Ghahramani, F., and Grønbæek, N.. "Derivations into iterated duals of Banach algebras." Studia Mathematica 128.1 (1998): 19-54. <http://eudml.org/doc/216473>.

@article{Dales1998,
abstract = {We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space $A^\{(n)\}$ is zero; i.e., $ℋ^1(A,A^\{(n)\}) = \{0\}$. Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study group algebras, C*-algebras, Banach function algebras, and algebras of operators. Our results are summarized and some open questions are raised in the final section.},
author = {Dales, H., Ghahramani, F., Grønbæek, N.},
journal = {Studia Mathematica},
keywords = {derivations; iterated duals of Banach algebras; cohomology group; amenability},
language = {eng},
number = {1},
pages = {19-54},
title = {Derivations into iterated duals of Banach algebras},
url = {http://eudml.org/doc/216473},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Dales, H.
AU - Ghahramani, F.
AU - Grønbæek, N.
TI - Derivations into iterated duals of Banach algebras
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 1
SP - 19
EP - 54
AB - We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space $A^{(n)}$ is zero; i.e., $ℋ^1(A,A^{(n)}) = {0}$. Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable; we study group algebras, C*-algebras, Banach function algebras, and algebras of operators. Our results are summarized and some open questions are raised in the final section.
LA - eng
KW - derivations; iterated duals of Banach algebras; cohomology group; amenability
UR - http://eudml.org/doc/216473
ER -

References

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Citations in EuDML Documents

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  1. A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki, Constructions preserving n -weak amenability of Banach algebras
  2. Alireza Medghalchi, Taher Yazdanpanah, Problems concerning n -weak amenability of a Banach algebra
  3. M. Eshaghi-Gordji, A. Ebadian, F. Habibian, B. Hayati, Weak * -continuous derivations in dual Banach algebras
  4. Eshaghi M. Gordji, F. Habibian, B. Hayati, Ideal amenability of module extensions of Banach algebras
  5. Fatemeh Anousheh, Davood Ebrahimi Bagha, Abasalt Bodaghi, Weak amenability for the second dual of Banach modules
  6. Abasalt Bodaghi, Behrouz Shojaee, A generalized notion of n -weak amenability

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