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Let be a Banach algebra. is called ideally amenable if for every closed ideal of , the first cohomology group of with coefficients in is zero, i.e. . Some examples show that ideal amenability is different from weak amenability and amenability. Also for , is called -ideally amenable if for every closed ideal of , . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.
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 -
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