Related papers: Nonlinear maps preserving the mixed Jordan triple …

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…

Let $\mathcal{A}$ be a factor with dim$\mathcal{A}\geq2$. For $A, B\in\mathcal{A}$, define by $[A, B]_{*}=AB-BA^{\ast}$ and $A\bullet B=AB+BA^{\ast}$ the new products of $A$ and $B$. In this paper, it is proved that a map $\Phi: \mathcal…

Let $\mathcal {A}$ be a unital $\ast$-algebra. For $A, B\in\mathcal{A}$, define by $[A, B]_{*}=AB-BA^{\ast}$ and $A\bullet B=AB+BA^{\ast}$ the new products of $A$ and $B$. In this paper, under some mild conditions on $\mathcal {A}$, it is…

Let $\phi: A\to A$ be a (not necessarily linear, additive or continuous) map of a standard operator algebra. Suppose for any $a,b\in A$ there is an algebra automorphism $\theta_{a,b}$ of $ A$ such that \begin{align*} \phi(a)\phi(b) =…

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…

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective nonlinear maps $\Phi :\mathcal{A}\rightarrow \mathcal{B}$…

We present some properties of (not necessarily linear) positive maps between $C^*$-algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between $C^*$-algebras. Then we give some basic properties and…

Let $\mathcal{A}$ and $\mathcal{B}$ be two alternative $W^{*}$-factors. In this paper, we proved that a bijective mapping $\Phi :\mathcal{A}\rightarrow \mathcal{B}$ satisfies $\Phi (ab+ba^{*})=\Phi (a)\Phi (b)+\Phi (b)\Phi (a)^{*}$ (resp.,…

Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$…

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that $\mathcal{B}$ is prime. In this paper, we investigate the additivity of map $\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and satisfies…

We study maps between positive definite or positive semidefinite cones of unital $C^*$-algebras. We describe surjective maps that preserve (1) the norm of the quotient or multiplication of elements; (2) the spectrum of the quotient or…

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial projections in $\mathfrak{A}$. In this paper we…

Let T be be a zero-product preserving bounded linear map between C*-algebras A and B. Here neither A nor B is necessarily unital. In this note, we investigate when T gives rise to a Jordan homomorphism. In particular, we show that A and B…

Let $\phi$ be a positive unital normal map of a von Neumann algebra $M$ into itself, and assume there is a family of normal $\phi$-invariant states which is faithful on the von Neumann algebra generated by the image of $\phi$. It is shown…

Let $\mathscr{R}$ be a finite von Neumann algebra with a faithful tracial state $\tau $ and let $\Delta$ denote the associated Fuglede-Kadison determinant. In this paper, we characterize all unital bijective maps $\phi$ on the set of…

Let $\mathcal{A}$ be a factor von Neumann algebra and $\phi$ be the $\ast$-Jordan derivation on $A$, that is, for every $A,B \in \mathcal{A}$, $\phi(A\diamond_{1} B) = \phi(A)\diamond_{1} B + A\diamond_{1}\phi( B)$ where $A\diamond_{1} B =…

Let $A$ and $B$ be Banach algebras with bounded approximate identities and let $\Phi:A\to B$ be a surjective continuous linear map which preserves two-sided zero products (i.e., $\Phi(a)\Phi(b)=\Phi(b)\Phi(a)=0$ whenever $ab=ba=0$). We show…

Let $M$ and $N$ be arbitrary von Neumann algebras. For any $a$ in $M$ or in $N$, let $\Delta_{\lambda}(a)$ denote the $\lambda$-Aluthge transform of $a$. Suppose that $M$ has no abelian direct summand. We prove that every bijective map…

Let $A$ be an algebra over a field $F$ with {\rm char}$(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the…

We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ strongly preserving Brown-Pedersen quasi-invertible…