483 research outputs found
Connes amenability of the second dual of Arens regular Banach algebras
In this paper we study the Connes amenability of the second dual of Arens
regular Banach algebras. Of course we provide a partial answer to the question
posed by Volker Runde. Also we fined the necessary and sufficient conditions
for the second dual of an Arens regular module extension Banach algebra to be
Connes amenable when the module is reflexive.Comment: 5 pages. To appear in Italian J. of Pure and Appl. Mat
Jordan homomorphisms between unital algebras
Let be two unital algebras. We prove that every almost unital
almost linear mapping which satisfies for all , all , and all , is a Jordan homomorphism. Also, for a unital algebra of real
rank zero, every almost unital almost linear continuous mapping
is a Jordan homomorphism when holds for all , all and
all . Furthermore, we investigate the Hyers--Ulam--Rassias
stability of Jordan homomorphisms between unital algebras by using
the fixed points methods
On approximate n-ring homomorphisms and n-ring derivations
Let be two rings and let be an module. An additive map is called n-ring homomorphism if
for all . An additive map is called
-ring derivation if for all . In this paper we investigate the Hyers-Ulam-Rassias stability of -ring
homomorphisms and n-ring derivations
Stability of a functional equation deriving from quartic and additive functions
In this paper, we obtain the general solution and the generalized Hyers-Ulam
Rassias stability of the functional equation
f(2x+y)+f(2x-y)=4(f(x+y)+f(x-y))-{3/7}(f(2y)-2f(y))+2f(2x)-8f(x).$
Left introverted subspaces of duals of Banach algebras and continuous derivations on dual Banach algebras
Let be a left introverted subspace of dual of a Banach algebra. We study
the topological center of Banach algebra . We fined the
topological center of (X\cA)^*, when \cA has a bounded right approximate
identity and \cA\subseteq X^*. So we introduce a new notation of amenability
for a dual Banach algebra . A dual Banach algebra is weakly
Connes-amenable if the first continuous cohomology group of
with coefficients in is zero; i.e., .
We study the weak Connes-amenability of some dual Banach algebras.Comment: 10 page
n-Jordan homomorphisms
Let and let be two rings. An additive map is
called n-Jordan homomorphism if for all . Every
Jordan homomorphism is an n-Jordan homomorphism, for all but the
converse is false, in general. In this paper we investigate the n-Jordan
homomorphisms on Banach algebras. Indeed some results related to continuity are
given as well
Derivations into n-th duals of ideals of Banach algebras
We introduce two notions of amenability for a Banach algebra . Let
and let be a closed two-sided ideal in , is
weakly amenable if the first cohomology group of with
coefficients in the n-th dual space is zero; i.e., . Further, is n-ideally amenable if is
weakly amenable for every closed two-sided ideal in . We find
some relationships of weak amenability and weak amenability for
some different m and n or for different closed ideals and of .Comment: 11 pag
Stability of cubic and quartic functional equations in non-Archimedean spaces
We prove generalized Hyres-Ulam-Rassias stability of the cubic functional
equation for all
and the quartic functional equation
for all in non-Archimedean normed spaces
Some applications of the generalized Bernardi - Libera - Livingston integral operator on univalent functions
In this paper by making use of the generalized Bernardi - Libera - Livingston
integral operator we introduce and study some new subclasses of univalent
functions. Also we investigate the relations between those classes and the
classes which are studied by Jin-Lin Liu
On the stability of generalized mixed type quadratic and quartic functional equation in quasi-Banach spaces
In this paper, we establish the general solution of the functional equation
f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0
cm}for fixed integers with and investigate the generalized
Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces
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