# 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

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topDales, 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 -

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## Citations in EuDML Documents

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- Alireza Medghalchi, Taher Yazdanpanah, Problems concerning $n$-weak amenability of a Banach algebra
- Eshaghi M. Gordji, F. Habibian, B. Hayati, Ideal amenability of module extensions of Banach algebras
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