n-WEAK AMENABILITY AND STRONG DOUBLE LIMIT PROPERTY

Title & Authors
n-WEAK AMENABILITY AND STRONG DOUBLE LIMIT PROPERTY
MEDGHALCHI, A.R.; YAZDANPANAH, T.;

Abstract
Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $\small{(a_\alpha)}$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta=lim_\beta\;lim_\alpha$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $\small{A^{\ast\ast}}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $\small{A^{\ast\ast}}$ is weakly amenable and A has the SDLP, then A is weakly amenable.
Keywords
Banach algebra;weak amenability;Arens regular;n-weak amenability;
Language
English
Cited by
1.
The third dual of a Banach algebra, Studia Scientiarum Mathematicarum Hungarica, 2008, 45, 1, 1
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