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n-WEAK AMENABILITY AND STRONG DOUBLE LIMIT PROPERTY
MEDGHALCHI, A.R.,YAZDANPANAH, T. Korean Mathematical Society 2005 대한수학회보 Vol.42 No.2
Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $(a_\alpha)$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta<a_\alpha,\;a^{\ast}\;_\beta>=lim_\beta\;lim_\alpha<a_\alpha,\;a^{\ast}\;_\beta>$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $A^{\ast\ast}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $A^{\ast\ast}$ is weakly amenable and A has the SDLP, then A is weakly amenable.
$n$-weak amenability and strong double limit property
A.R. Medghalchi,T. Yazdanpanah 대한수학회 2005 대한수학회보 Vol.42 No.2
Let {mathcal A} be a Banach algebra, we say that {mathcalA}has the strongly double limit property (SDLP) if for each boundednet (a_{alpha}) in {mathcal A} and each bounded net(a^*_{beta}) in {mathcal A}^*, lim_{alpha}lim_{beta}leftlangle a_{alpha} , a^*_{beta}rightrangle = lim_{beta} lim_{alpha} leftlangle a_{alpha}, a^*_{beta} rightrangle whenever both iterated limits exist. In this paperamong other results we show that if {mathcal A} has the SDLP and{mathcal A}^{**} is (n-2)-weakly amenable, then {mathcal A} isn-weakly amenable. In particular, it is shown that if {mathcalA}^{**} is weakly amenable and {mathcal A} has the SDLP, then ${\mathcal A}$ is weakly amenable
SEMI-ASYMPTOTIC NON-EXPANSIVE ACTIONS OF SEMI-TOPOLOGICAL SEMIGROUPS
Amini, Massoud,Medghalchi, Alireza,Naderi, Fouad Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
In this paper we extend Takahashi's fixed point theorem on discrete semigroups to general semi-topological semigroups. Next we define the semi-asymptotic non-expansive action of semi-topological semi-groups to give a partial affirmative answer to an open problem raised by A.T-M. Lau.
Semi-asymptotic non-expansive actions of semi-topological semigroups
Massoud Amini,Alireza Medghalchi 대한수학회 2016 대한수학회보 Vol.53 No.1
In this paper we extend Takahashi's fixed point theorem on discrete semigroups to general semi-topological semigroups. Next we define the semi-asymptotic non-expansive action of semi-topological semigroups to give a partial affirmative answer to an open problem raised by A.T-M. Lau.