Geodesic
Derivations into iterated duals of Banach algebras
Studia Mathematica, Tome 128 (1998) no. 1, pp. 19-54

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-128-1-19-54

H. G. Dales 1 ;  1 ;  1

1 
@article{10_4064_sm_128_1_19_54,
     author = {H. G. Dales and   and  },
     title = {Derivations into iterated duals of {Banach} algebras},
     journal = {Studia Mathematica},
     pages = {19--54},
     publisher = {mathdoc},
     volume = {128},
     number = {1},
     year = {1998},
     doi = {10.4064/sm-128-1-19-54},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-128-1-19-54/}
}
TY  - JOUR
AU  - H. G. Dales
AU  -  
AU  -  
TI  - Derivations into iterated duals of Banach algebras
JO  - Studia Mathematica
PY  - 1998
SP  - 19
EP  - 54
VL  - 128
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-128-1-19-54/
DO  - 10.4064/sm-128-1-19-54
LA  - en
ID  - 10_4064_sm_128_1_19_54
ER  - 
%0 Journal Article
%A H. G. Dales
%A  
%A  
%T Derivations into iterated duals of Banach algebras
%J Studia Mathematica
%D 1998
%P 19-54
%V 128
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-128-1-19-54/
%R 10.4064/sm-128-1-19-54
%G en
%F 10_4064_sm_128_1_19_54
H. G. Dales;  ;  . Derivations into iterated duals of Banach algebras. Studia Mathematica, Tome 128 (1998) no. 1, pp. 19-54. doi: 10.4064/sm-128-1-19-54

Cité par Sources :