Let A,B be two unital C∗−algebras. We prove that every almost unital almost linear mapping h : A −→ B which satisfies h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ..., is a Jordan homomorphism. Also, for a unital C∗−algebra A of real rank zero, every almost unital almost linear continuous mapping h : A −→ B is a Jordan homomorphism when h(3uy + 3yu) = h...

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

1. Introduction. One may construct a Jordan homomorphism from one (associative) ring into another ring by taking the sum of a homo-morphism and an antihomomorphism of the first ring into two ideals in the second ring with null intersection [6]. A number of authors have considered conditions on the rings that imply that every Jordan homomorphism, or isomorphism, is of this form [6], [3], [7], [1...

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

Let θ : A → B be a zero-product preserving bounded linear map between C*-algebras. Here neither A nor B is necessarily unital. In this note, we investigate when θ gives rise to a Jordan homomorphism. In particular, we show that A and B are isomorphic as Jordan algebras if θ is bijective and sends zero products of self-adjoint elements to zero products. They are isomorphic as C*-algebras if θ is...

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

We investigate linear operators between C?-algebras which approximately preserve involution and orthogonality, the latter meaning that for some ?>0 we have ??(x)?(y)????x??y? all positive x,y with xy=0. establish structural properties of such maps concerning approximate Jordan-like equations almost commutation relations. In situations (e.g. when codomain is finite-dimensional), show ? can be ap...