相关论文: Commutativity preservers of incidence algebras

Let $X$ be a finite connected poset, $F$ a field and $I(X,F)$ the incidence algebra of $X$ over $F$. We describe the bijective linear idempotent preservers $\varphi:I(X,F)\to I(X,F)$. Namely, we prove that, whenever $\mathrm{char}(F)\ne 2$,…

Let $A$, $B$ be algebras and $a\in A$, $b\in B$ a fixed pair of elements. We say that a map $\varphi:A\to B$ preserves products equal to $a$ and $b$ if for all $a_1,a_2\in A$ the equality $a_1a_2=a$ implies $\varphi(a_1)\varphi(a_2)=b$. In…

Let $X$ be an arbitrary poset and $K$ an arbitrary field. We describe linear unital invertibility preservers of the finitary incidence algebra $FI(X,K)$ in terms of certain maps of the power set algebra $\mathcal{P}(X)$ and linear maps…

In the first part of the paper we describe $\varphi$-derivations of the incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$, where $\varphi$ is an arbitrary automorphism of $I(X,K)$. We show that they admit…

Let ${\mathcal M}$ be a von Neumann algebra without central summands of type $I_1$. Assume that $\Phi:{\mathcal M}\rightarrow {\mathcal M}$ is a surjective map. It is shown that $\Phi$ is strong skew commutativity preserving (that is,…

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, in…

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain…

Let ${\mathcal M}_2(\mathbb F)$ be the algebra of 2$\times$2 matrices over the real or complex field $\mathbb F$. For a given positive integer $k\geq 1$, the $k$-commutator of $A$ and $B$ is defined by $[A,B]_k=[[A,B]_{k-1},B]$ with…

Let $X$ be a Banach space of dimension $\geq 2$ over the real or complex field ${\mathbb F}$ and ${\mathcal A}$ a standard operator algebra in ${\mathcal B}(X)$. A map $\Phi:{\mathcal A} \rightarrow {\mathcal A}$ is said to be strong…

Let $X$ be a finite connected poset, $K$ a field of characteristic zero and $I(X,K)$ the incidence algebra of $X$ over $K$ seen as a Lie algebra under the commutator product. In the first part of the paper we show that any…

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $\chi_\alpha^2$-divergence for some $\alpha \in…

Maps that preserve adjacency on the set of all invertible hermitian matrices over a finite field are characterized. It is shown that such maps form a group that is generated by the maps $A\mapsto PAP^{\ast}$, $A\mapsto A^{\sigma}$, and…

Let $A$ and $B$ be unital complex Banach algebras having no quotients isomorphic to $\mathbb{C}$ or $M_2(\mathbb{C})$. Assume additionally that $B$ is semisimple. If a surjective additive mapping $\Phi\colon A\to B$ satisfies…

Let $\varphi$ be a holomorphic map which is a symbol of a bounded composition operator $C_\varphi$ acting on the Hardy-Hilbert space of Dirichlet series. We find a K\"onigs map for $\varphi$. We then deduce several applications on…

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, we…

We resolve an algebraic version of Schoenberg's celebrated theorem [Duke Math.J., 1942] characterizing entrywise matrix transforms that preserve positive definiteness. Compared to the classical real and complex settings, we consider…

Let $p\geq3$ be a prime and $e\geq2$ an integer. Let $\sigma(x)$ be a primitive polynomial of degree $n$ over $Z/p^eZ$ and $G'(\sigma(x),p^e)$ the set of primitive linear recurring sequences generated by $\sigma(x)$. A compressing map…

Let $C_\varphi$ be a composition operator acting on the Hardy space of the unit disc $H^p$ ($1\leq p < \infty$), which is embedded in a $C_0$-semigroup of composition operators $\mathcal{T}=(C_{\varphi_t})_{t\geq 0}.$ We investigate whether…

Suppose $\mathfrak{R}$ is a $2$,$3$-torsion free unital alternative ring having an idempotent element $e_1$ $\left(e_2 = 1-e_1\right)$ which satisfies $x \mathfrak{R} \cdot e_i = \{0\} \rightarrow x = 0$ $\left(i = 1,2\right)$. In this…