Related papers: On linear preservers of semipositive matrices

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

We prove the linearity and injectivity of two maps $\phi_1$ and $\phi_2$ on certain subsets of $M_n$ that satisfy $\operatorname{tr}(\phi_1(A)\phi_2(B))=\operatorname{tr}(AB)$. We apply it to characterize maps $\phi_i:\mathcal{S}\to…

Given two elements $A,B$ in a compact semisimple Lie algebra, we show that there is a regular element $X$ and elements $Y,Z$ with $A=[X,Y]$ and $B=[X,Z]$. In the course of the proof we show also that every linear subspace $V$ of codimension…

Let $S$ be the multiplicative semigroup of $q\times q$ matrices with positive entries such that every row and every column contains a strictly positive element. Denote by $(X_n)_{n\geq1}$ a sequence of independent identically distributed…

We study the left-right action of $\operatorname{SL}_n \times \operatorname{SL}_n$ on $m$-tuples of $n \times n$ matrices with entries in an infinite field $K$. We show that invariants of degree $n^2- n$ define the null cone. Consequently,…

Linear preserver problems have been a central focus of research in matrix theory and operator theory for more than a century, beginning with Frobenius' 1897 characterization of determinant preserving linear maps on the space of complex…

For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different…

A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be expressed as a# b where a and b are elements of S and if, in addition, every element of S that is square…

This work characterizes the general form of a bijective linear map $\Psi:\mathscr{M}_n(\mathbb{C}) \to \mathscr{M}_n(\mathbb{C})$ such that $[\Psi(A_1),~\Psi(A_2)]=D_2$ whenever $[A_1,~A_2]=D_1$ where $D_1~\text{and}~D_2$ are fixed…

In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…

In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, K], then either…

Let $K_1 \subset H$ and $K_2 \subset H$ be half-sided modular inclusions in a common standard subspace $H$. We prove that the inclusion $K_1 \subset K_2$ holds if and only if we have an inclusion of spectral subspaces of the generators of…

Let $k$ be an arbitrary field and $d$ a positive integer. For each degenerate symmetric or antisymmetric bilinear form $M$ on $k^{d}$ we determine the structure of the Lie algebra of matrices that preserve $M$, and of the Lie algebra of…

We study the problem of when the continuous linear image of a fixed closed convex set $X \subset\mathbb{R}^n$ is closed. Specifically, we improve the main results in the papers \cite{Borwein2009, Borwein2010} by showing that for all, except…

A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a semiring $S$ is uniserial if and only if the matrix semiring $M_n(S)$ is uniserial. As a generalization of valuation semirings, we also…

Let K be an arbitrary (commutative) field with at least three elements. It was recently proven that an affine subspace of M_n(K) consisting only of non-singular matrices must have a dimension lesser than or equal to n(n-1)/2. Here, we…

We study $k$-positive linear maps on matrix algebras and address two problems, (i) characterizations of $k$-positivity and (ii) generation of non-decomposable $k$-positive maps. On the characterization side, we derive optimization-based…

This paper is the second in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belonging to an arbitrary ground field which is large enough. In…

Two (real or complex) $m\times n$ matrices $A$ and $B$ are said to be parallel (resp. triangle equality attaining, or TEA in short) with respect to the spectral norm $\|\cdot\|$ if $\|A+ \mu B\| = \|A\| + \|B\|$ for some scalar $\mu$ with…

In this paper a complete description of the linear maps $\phi:W_{n}\rightarrow W_{n}$ that preserve the Lorentz spectrum is given when $n=2$ and $W_{n}$ is the space $M_{n}$ of $n\times n$ real matrices or the subspace $S_{n}$ of $M_{n}$…