Related papers: Nonlinear mixed Jordan triple *-derivations on fac…

Let $M_n$ be the algebra of $n \times n$ complex matrices. We consider arbitrary subalgebras $\mathcal{A}$ of $M_n$ which contain the algebra of all upper-triangular matrices (i.e.\ block upper-triangular subalgebras), and their Jordan…

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X of dimension at least three. For an arbitrary nonzero complex number t we determine the form of mappings f: B(X)-->B(X) with sufficiently large range such…

The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear maps including derivations, Lie derivations and Jordan derivations. In this paper we introduce the notion of f-biderivations as a natural…

Let $M_n(R)$ be the algebra of all $n\times n$ matrices over a unital commutative ring $R$ with 6 invertible. We say that $A\in M_n(R)$ is a Jordan product determined point if for every $R$-module $X$ and every symmetric $R$-bilinear map…

Let $\mathcal{A}$ be a unital Banach $*$-algebra and $\mathcal{M}$ be a unital $*$-$\mathcal{A}$-bimodule. If $W$ is a left separating point of $\mathcal{M}$, we show that every $*$-derivable mapping at $W$ is a Jordan derivation, and every…

Let $X_1$ and $X_2$ be complex Banach spaces with dimension at least three, $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on $X_1$ and $X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms…

A linear map $\Phi :\mathbb{M}_n \to \mathbb{M}_k$ is called completely copositive if the resulting matrix $[\Phi (A_{j,i})]_{i,j=1}^m$ is positive semidefinite for any integer $m$ and positive semidefinite matrix $[A_{i,j}]_{i,j=1}^m$. In…

Let $\mathfrak{M}(\mathbb{D}, m, n, P)$ be the ring of all $m \times n$ matrices over a division ring $\mathbb{D}$, with the product given by $A \bullet B=A P B$, where $P$ is a fixed $n \times m$ matrix over $\mathbb{D}$. When $2\leq m, n…

Let $X$ be a locally finite partially ordered set (poset), $K$ a field of characteristic not 2, and $I(X,K)$ the incidence algebra over $K$. In this paper, we prove that every Jordan $*$-derivation of $I(X,K)$ is an inner $*$-derivation and…

Let $\Mn$ be the ring of all $n \times n$ matrices over a unital ring $\mathcal{R}$, let $\mathcal{M}$ be a 2-torsion free unital $\Mn$-bimodule and let $D:\Mn\rightarrow \mathcal{M}$ be an additive map. We prove that if $D(\A)\B+ \A…

In this article, we give a complete characterization of the bijective maps which commute with the mean transform under Jordan product. The main result is the following : Let $H,K$ be two complex Hilbert spaces and $\Phi :B(H) \to B(K)$ be a…

Let $P$ be a preordered set, $R$ a ring and $FI(P,R)$ the finitary incidence ring of $P$ over $R$. We find a criterion for all Jordan derivations of $FI(P,R)$ to be derivations and generalize Theorem 3.3 from arXiv:1411.6123. In particular,…

In the paper "Maps preserving the spectrum of generalized Jordan product of operators", we define a generalized Jordan products on standard operator algebras $A_1, A_2$ on complex Banach spaces $X_1, X_2$, respectively. This includes the…

Let $\eta\neq -1$ be a non-zero complex number, and let $\phi$ be a not necessarily linear bijection between two von Neumann algebras, one of which has no central abelian projections preserving the Jordan $\eta$-$\ast$-$n$-product. It is…

There exists a generalization of the concept, completely bounded norm for multilinear maps on C*-algebras. We will use the word, Jordan norm, for this norm. The Jordan norm of a multilinear map is obtained via factorizations of the map,…

In this paper, we characterize Jordan derivable mappings in terms of Peirce decomposition and determine Jordan all-derivable points for some general bimodules. Then we generalize the results to the case of Jordan higher derivable mappings.…

This paper presents some results on simple exceptional Jordan algebra over algebraically closed field $\Phi$ with characteristic not 2. Namely an example of simple decomposition of $H(O_3)$ into the sum of two subalgebras of the type…

A map $\phi$ on an associative ring is called a multiplicative Lie derivation if $\phi([x,y])=[\phi(x),y]+[x,\phi(y)]$ holds for any elements $x,y$, where $[x,y]=xy-yx$ is the Lie product. In the paper, we discuss the multiplicative Lie…

Let $\mathcal R$ be a ring, $\mathcal{M}$ be a $\mathcal R$-bimodule and $m,n$ be two fixed nonnegative integers with $m+n\neq0$. An additive mapping $\delta$ from $\mathcal R$ into $\mathcal{M}$ is called an \emph{$(m,n)$-Jordan…

Let $\T$ be a $2$-torsion free triangular ring and let $\varphi:\T\rightarrow \T$ be an additive map. We prove that if $\A \varphi(\B)+\varphi(\B)\A=0$ whenever $\A,\B\in \T$ are such that $\A\B=\B\A=0$, then $\varphi$ is a centralizer. It…