Related papers: A spectral radius for matrices over an operator sp…

For any motivic $\mathbb{E}_\infty$-ring spectrum $A$ we construct an equivalence $\rho$ between the $\infty$-category of cellular motivic $A$-module spectra and modules over an $\mathbb{E}_1$-algebra $\Theta$ in $\mathbb{Z} $-graded…

We show how the essential spectral radius of a bounded positive kernel, acting on bounded functions, is linked to its lower approximation by certain absolutely continuous kernels. The standart Doeblin's condition can be interpreted in this…

We consider a positive and power-bounded linear operator $T$ on $L^p$ over a finite measure space and prove that, if $TL^p \subseteq L^q$ for some $q > p$, then the essential spectral radius of $T$ is strictly smaller than $1$. As a special…

In this paper, we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional. We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on even-dimensional…

This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism $f$, an \( f \)-compatible matrices capture aspects of the symmetry, represented…

Let $G$ be a simple graph, and denote by $\lambda(G)$ its spectral radius. Sun and Das (2020) established that for any non-isolated vertex $v$ with degree $d(v)$, \[ \lambda(G)\leq \sqrt{\lambda(G-v)^2 + 2d(v) - 1}, \] which is a conjecture…

It is well known that the spectral radius of a tree whose maximum degree is $D$ cannot exceed $2\sqrt{D-1}$. In this paper we derive similar bounds for arbitrary planar graphs and for graphs of bounded genus. It is proved that a the…

This paper concerns the spectral properties of the Neumann-Poincar\'e operator on $m$-fold rotationally symmetric planar domains. An $m$-fold rotationally symmetric simply connected domain $D$ is realized as the $m$th-root transform of a…

In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterates of Aluthge transformation, numerical radius and the asymptotic behavior of the powers of this operator. Also we…

In this paper, it is shown that with large probability, the spectral radius of a large non-Hermitian random matrix with a general variance profile does not exceed the square root of the spectral radius of the variance profile matrix. A…

Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup $\bS^+$ restricted to a…

This paper aims to provide an explicit computation of the spectral torsion associated with the Connes type operator on even dimension compact manifolds.And we also extend the spectral torsion for the Connes type operator to compact…

We study the finite-step realizability of the joint/generalized spectral radius of a pair of real $d\times d$ matrices, one of which has rank 1. Then we prove that there always exists a finite-length word for which there holds the spectral…

We solve completely the spectral synthesis problem for reproducing kernels in the de Branges spaces $\mathcal{H}(E)$. Namely, we describe the de Branges spaces $\mathcal{H}(E)$ such that all $M$-bases of reproducing kernels (i.e., complete…

For finite-dimensional operator systems $\mathcal{S}_{\mathsf T}$, ${\mathsf T} \in B({\mathcal H})^d$, we show that the local lifting property and $1$-exactness of $\mathcal{S}_{\mathsf T}$ may be characterized by measurements of the…

In this paper, we consider a general discrete-time spectral factorization problem for rational matrix-valued functions. We build on a recent result establishing existence of a spectral factor whose zeroes and poles lie in any pair of…

We extend the proof in [M.~Crouzeix and C.~Palencia, {\em The numerical range is a $(1 + \sqrt{2})$-spectral set}, SIAM Jour.~Matrix Anal.~Appl., 38 (2017), pp.~649-655] to show that other regions in the complex plane are $K$-spectral sets.…

Suppose $A=[a_{ij}]\in \mathcal{M}_n(\mathbb{C})$ is a complex $n \times n$ matrix and $B\in \mathcal{B}(\mathcal{H})$ is a bounded linear operator on a complex Hilbert space $\mathcal{H}$. We show that $w(A\otimes B)\leq w(C),$ where…

This article provides a systematic investigation of the minimum modulus of dual truncated Toeplitz operators (DTTOs) $D_{\varphi}$ acting on the orthogonal complement of the model space $\mathcal{K}_u^{\perp}$, where $u$ is a nonconstant…

We obtain various upper bounds for the numerical radius $w(T)$ of a bounded linear operator $T$ defined on a complex Hilbert space $\mathcal{H}$, by developing the upper bounds for the $\alpha$-norm of $T$, which is defined as…