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

top
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

top

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

top
  1. Bade W. G., Curtis P. G., Dales H. G.,, Amenability and weak amenability for Beurling and Lipschits algebra, Proc. London Math. Soc. (3) 55 (1987), 359–377. (1987) MR0896225
  2. Dales H. G., Ghahramani F., Grønbæk N., Derivations into iterated duals of Banach algebras, Studia Math. 128 (1998), 19–54. (1998) MR1489459
  3. Despic M., Ghahramani F., Weak amenability of group algebras of locally compact groups, Canad. Math. Bull. 37 (1994), 165–167. (1994) Zbl0813.43001MR1275699
  4. Eshaghi Gordji M., Hosseiniun S. A. R., Ideal amenability of Banach algebras on locally compact groups, Proc. Indian Acad. Sci. 115, 3 (2005), 319–325. Zbl1098.46033MR2161735
  5. Eshaghi Gordji M., Hayati B., Hosseiniun S. A. R., Derivations into duals of closed ideals of Banach algebras, submitted. 
  6. Eshaghi Gordji M., Habibian F., Rejali A., Ideal amenability of module extension Banach algebras, Int. J. Contemp. Math. Sci. 2, 5 (2007), 213–219. Zbl1120.46308MR2296773
  7. Eshaghi Gordji M., Memarbashi R., Derivations into n-th duals of ideals of Banach algebras, submitted. Zbl1154.46026
  8. Eshaghi Gordji M., Yazdanpanah T., Derivations into duals of ideals of Banach algebras, Proc. Indian Acad. Sci. 114, 4 (2004), 399–408. MR2067702
  9. Grønbæk N., A characterization of weakly amenable Banach algebras, Studia Math. 94 (1989), 150–162. (1989) MR1025743
  10. Grønbæk N., Weak and cyclic amenability for non-commutative Banach algebras, Proc. Edinburg Math. Soc. 35 (1992), 315–328. (1992) MR1169250
  11. Haagerup U., All nuclear 𝒞 * -algebras are amenable, Invent. Math. 74 (1983), 305–319. (1983) MR0723220
  12. Johnson B. E., Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). (1972) Zbl0256.18014MR0374934
  13. Johnson B. E., Weak amenability of group algebras, Bull. London Math. Soc. 23 (1991), 281–284. (1991) Zbl0757.43002MR1123339
  14. Johnson B. E., White M. C., A non-weakly amenable augmentation ideal, submitted. 
  15. Wassermann S., On tensor products of certain group C * - algebras, J. Funct. Anal. 23 (1976), 28–36. (1976) Zbl0358.46040MR0425628
  16. Zhang, Yong, Weak amenability of module extensions of Banach algebras, Trans. Amer. Math. Soc. 354, (10) (2002), 4131–4151. Zbl1008.46019MR1926868

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.