Related papers: Linear maps preserving matrices annihilated by a f…

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X with dim X greater than 3. In this paper, we characterize the forms of surjective linear maps on B(X) which preserve the dimension of the vector space…

Let $\mathbb V$ be an arbitrary linear space and $f:\mathbb V \times \ldots \times \mathbb V \to \mathbb V$ an $n$-linear map. It is proved that, for each choice of a basis ${\mathcal B}$ of $\mathbb V$, the $n$-linear map $f$ induces a…

Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive…

Let $R$ be a 2-torsion free unital ring and $N_n=N_n(R)$ the ring of strictly upper triangular matrices with entries in $R$ and center $Z=Z(N_n)$. It has been previously shown that any linear map $f:N_n\rightarrow N_n$ satisfying the…

Let $M_n(\mathbb{F})$ denote the algebra of $n \times n$ matrices over an algebraically closed field $\mathbb{F}$ of characteristic different from $2$. For $n \ge 2$, we classify all maps $\phi : M_n(\mathbb{F}) \to M_n(\mathbb{F})$…

A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…

A non-zero $\mathbb{F}$-valued $\mathbb{F}$-linear map on a finite dimensional $\mathbb{F}$-algebra is called an $\mathbb{F}$-valued trace if its kernel does not contain any non-zero ideals. However, given an $\mathbb{F}$-algebra such a map…

A partial description of the structure of positive unital maps $\phi: M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.

Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots,…

Let $f=f(x_1,\dots,x_m)$ be a multilinear polynomial over a field $F$. An $F$-algebra $A$ is said to be $f$-zpd ($f$-zero product determined) if every $m$-linear functional $\varphi\colon A^{m}\rightarrow F$ which preserves zeros of $f$ is…

Let $A$ be a $C^*$-algebra. Let $E$ and $F$ be Hilbert $A$-modules with $E$ being full. Suppose that $\theta : E\to F$ is a linear map preserving orthogonality, i.e., $<\theta(x), \theta(y) > = 0$ whenever $<x, y > = 0$. We show in this…

In this paper we characterize those linear bijective maps on the monoid of all $n \times n$ square matrices over an anti-negative semifield which preserve and strongly preserve each of Green's equivalence relations $\mathcal{L},…

It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization…

We determine the group of linear transformations on a vector space $V$ that preserve a polynomial function $f$ on $V$ for several interesting pairs $(V,f)$, using the theory of semisimple algebraic groups.

We characterize maps $\phi_i: \mathcal{S} \to \mathcal{S}$, $i=1, \ldots, m$ and $m\ge 1$, that have the multiplicative spectrum or trace preserving property: \begin{eqnarray*} \textrm{spec} (\phi_1(A_1)\cdots \phi_m(A_m)) &=& \textrm{spec}…

In this paper, we generalize some matrix inequalities involving matrix power and Karcher means of positive definite matrices. Among other inequalities, it is shown that if ${\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive definite…

We provide a characterisation of Schur multiplicative maps on both finite and infinite dimensional matrix spaces, and show that every surjective Schur multiplicative contraction is automatically an isometry. We also generalise this result…

We prove that a linear mapping on the algebra \(\mathfrak{sl}_n\) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an anti-automorphism. We also show that a linear mapping on a simple…

In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the…

We consider a tuple $\Phi = (\phi_1,\ldots,\phi_m)$ of commuting maps on a finitary matroid $X$. We show that if $\Phi$ satisfies certain conditions, then for any finite set $A\subseteq X$, the rank of $\{\phi_1^{r_1}\cdots\phi_m^{r_m}(a):a…