Related papers: Linear maps on $M_n(\mathbb{R})$ preserving Schur …

In this paper we prove that the generalization to $\mathbb{RP}^n$ of the pentagram map defined in \cite{KS} is invariant under certain scalings for any $n$. This property allows the definition of a Lax representation for the map, to be used…

The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point $z$ away from the…

Let $A$ be a square random matrix of size $n$, with mean zero, independent but not identically distributed entries, with variance profile $S$. When entries are i.i.d. with unit variance, the spectral radius of $n^{-1/2}A$ converges to $1$…

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…

We show that $J-$ stability is open and dense in natural families of meromorphic maps of one complex variable with a finite number of singular values, and even more generally, to finite type maps. This extends the results of…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

A matrix convex set is a set of the form $\mathcal{S} = \cup_{n\geq 1}\mathcal{S}_n$ (where each $\mathcal{S}_n$ is a set of $d$-tuples of $n \times n$ matrices) that is invariant under UCP maps from $M_n$ to $M_k$ and under formation of…

We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also…

Let $G$ be a simple connected graph with order $n$. Let $\mathcal{L}(G)$ be the normalized Laplacian matrix of $G$. Let $\lambda_{k}(G)$ be the $k$-th smallest normalized Laplacian eigenvalue of $G$. Denote $\rho(A)$ the spectral radius of…

Suppose that $M$ is a Riemann surface with boundary $\partial M$, $\Lambda$ is its DN-map, and $\mathscr E:M\to\mathbb{C}^{n}$ % $\mathfrak{J}_{M}$ is a holomorphic immersion. Let $M'$ be diffeomorphic to $M$, $\partial M=\partial M'$; let…

For each ideal of multilinear mappings $\cal M$ we explicitly construct a corresponding ideal $^{a}{\cal M}$ such that multilinear forms in $^{a}{\cal M}$ are exactly those which can be approximated, in the uniform norm, by multilinear…

We investigate the stabilizability of linear discrete-time switched systems with singular matrices, focusing on the spectral radius in this context. A new lower bound of the stabilizability radius is proposed, which is applicable to any…

The following two results are shown. 1) Let $G$ be the $k$-rational points of a simple algebraic group over a local field $k$ and let $H$ be a lattice in $G.$ Then the regular representation of $G$ on $L^2(G/H)$ has a spectral gap (that is,…

The spectrum of a density matrix $\rho(t)$ is conserved by a Lie-Nambu dynamics if $\rho(t)$ is a self-adjoint and Hilbert-Schmidt solution of a nonlinear triple-bracket equation. This generalizes to arbitrary separable (positive- and…

Let A be a unital algebra over a commutative unital ring R. We say that A is a SLIP algebra if every R-linear map on A that leaves invariant every left ideal of A is a left multiplier. In this paper we study whether a triangular algebra…

The existence of smooth families of Lorenz maps exhibiting all possible dynamical behavior is established and the structure of the parameter space of these families is described.

Let $B(H)$ be the algebra of all bounded linear operators on infinite-dimensional complex Hilbert space $H$. For $T, S \in B(H)$ denote by $T\bullet S=TS+ST^{\ast}$ and $[T\circ S]_{\ast}=TS-ST^{\ast}$ the Jordan $\ast$-product and the skew…

Starting from Sinclair's 1976 work {\it Automatic Continuity of Linear Operators}, Cambridge University Press, (1976), on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear…

Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an…

For a smooth expanding map $f$ of the circle, its (unmarked) length spectrum is defined as the set of logarithms of multipliers of periodic orbits of $f$. This spectrum is analogous to the set of lengths of all closed geodesics on…