Using fixed pointmethods, we investigate approximately higher ternary Jordan derivations in Banach ternaty algebras via the Cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to ...

Unless we say otherwise, every vector space we talk about is taken to be over C. A Banach algebra is a Banach space A that is also an algebra satisfying ‖AB‖ ≤ ‖A‖ ‖B‖ for A,B ∈ A. We say that A is unital if there is a nonzero element I ∈ A such that AI = A and IA = A for all A ∈ A, called a identity element. If X is a Banach space, let B(X) denote the set of bounded linear operators X → X, and...

A theorem is presented on existence and uniqueness up to the topological *-isomorphism of universal locally C*-algebra for an arbitrary locally JB-algebra. The abstract Banach associative symmetrical *-algebras over C, so called C*algebras, were introduces first by Gelfand and Naimark in []. In the present time the theory of C*-algebras become a vast portion of Functional Analysis having connec...

We give a description of the continuity ideals and the kernels of homomorphisms from the algebras of continuous functions on locally compact spaces into Banach algebras.

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to ...

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

In this paper, we introduce the notion of multi-fuzzy normed spaces and establish an asymptotic behavior of the quadratic functional equations in the setup of such spaces. We then investigate the superstability of strongly higher derivations in the framework of multi-fuzzy Banach algebras