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Ideal amenability of module extensions of Banach algebras

Eshaghi M. Gordji; F. Habibian; B. Hayati

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 3, page 177-184
  • ISSN: 0044-8753

Abstract

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Let 𝒜 be a Banach algebra. 𝒜 is called ideally amenable if for every closed ideal I of 𝒜 , the first cohomology group of 𝒜 with coefficients in I * is zero, i.e. H 1 ( 𝒜 , I * ) = { 0 } . Some examples show that ideal amenability is different from weak amenability and amenability. Also for n N , 𝒜 is called n -ideally amenable if for every closed ideal I of 𝒜 , H 1 ( 𝒜 , I ( n ) ) = { 0 } . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.

How to cite

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Gordji, Eshaghi M., Habibian, F., and Hayati, B.. "Ideal amenability of module extensions of Banach algebras." Archivum Mathematicum 043.3 (2007): 177-184. <http://eudml.org/doc/250181>.

@article{Gordji2007,
abstract = {Let $\mathcal \{A\}$ be a Banach algebra. $\mathcal \{A\}$ is called ideally amenable if for every closed ideal $I$ of $\mathcal \{A\}$, the first cohomology group of $\mathcal \{A\}$ with coefficients in $I^*$ is zero, i.e. $H^1(\{\mathcal \{A\}\}, I^*)=\lbrace 0\rbrace $. Some examples show that ideal amenability is different from weak amenability and amenability. Also for $n\in \{N\}$, $\mathcal \{A\}$ is called $n$-ideally amenable if for every closed ideal $I$ of $\mathcal \{A\}$, $H^1(\{\mathcal \{A\}\},I^\{(n)\})=\lbrace 0\rbrace $. In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.},
author = {Gordji, Eshaghi M., Habibian, F., Hayati, B.},
journal = {Archivum Mathematicum},
keywords = {ideally amenable; Banach algebra; derivation; ideally amenable; Banach algebra; derivation},
language = {eng},
number = {3},
pages = {177-184},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Ideal amenability of module extensions of Banach algebras},
url = {http://eudml.org/doc/250181},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Gordji, Eshaghi M.
AU - Habibian, F.
AU - Hayati, B.
TI - Ideal amenability of module extensions of Banach algebras
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 3
SP - 177
EP - 184
AB - Let $\mathcal {A}$ be a Banach algebra. $\mathcal {A}$ is called ideally amenable if for every closed ideal $I$ of $\mathcal {A}$, the first cohomology group of $\mathcal {A}$ with coefficients in $I^*$ is zero, i.e. $H^1({\mathcal {A}}, I^*)=\lbrace 0\rbrace $. Some examples show that ideal amenability is different from weak amenability and amenability. Also for $n\in {N}$, $\mathcal {A}$ is called $n$-ideally amenable if for every closed ideal $I$ of $\mathcal {A}$, $H^1({\mathcal {A}},I^{(n)})=\lbrace 0\rbrace $. In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.
LA - eng
KW - ideally amenable; Banach algebra; derivation; ideally amenable; Banach algebra; derivation
UR - http://eudml.org/doc/250181
ER -

References

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