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

In this paper we show a characterization of the joint spectral radius of a set of matrices as the limit of the $p$-radius of an associated probability distribution when $p$ tends to $\infty$. Allowing the set to have infinitely many…

The spectral abscissa is the largest real part of an eigenvalue of a matrix and the spectral radius is the largest modulus. Both are examples of spectral max functions---the maximum of a real-valued function over the spectrum of a matrix.…

Spectral spaces, introduced by Hochster, are topological spaces homeomorphic to the prime spectra of commutative rings. In this paper we study spectral spaces in perspective of idempotent semirings which are algebraic structures receiving a…

Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectrums of these…

Let $\mathcal{G}_{n, \beta^*}$ $(\mathcal{G}^*_{n,\beta^*})$ be the set of all (connected) graphs of order $n$ with fractional matching number $\beta^*$. In this paper, the graphs with maximal spectral radius in $\mathcal{G}_{n,\beta^*}$…

We study rectangular Vandermonde matrices $\mathbf{V}$ with $N+1$ rows and $s$ irregularly spaced nodes on the unit circle, in cases where some of the nodes are "clustered" together -- the elements inside each cluster being separated by at…

Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the…

We provide a characterization of the spectral minimum for a random Schr\"odinger operator of the form $H=-\Delta + \sum_{i \in \Z^d}q(x-i-\omega_i)$ in $L^2(\R^d)$, where the single site potential $q$ is reflection symmetric, compactly…

We argue that the Schwarzschild-de Sitter black hole entropy formula does not imply that the entanglement spectrum of the vacuum density matrix of de Sitter space is flat. Specifically, we show that the expectation value of a random…

We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…

We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices…

In a bounded domain $G$ with smooth border studied boundary value and spectral problems for operators of the rotor (vortex) and the gradient of the divergence $+\lambda\,I$ in the Sobolev spaces. For $\lambda\neq 0$ these operators are…

We analyze spectral properties of the Hilbert $L$-matrix $$\left(\frac{1}{\max(m,n)+\nu}\right)_{m,n=0}^{\infty}$$ regarded as an operator $L_{\nu}$ acting on $\ell^{2}(\mathbb{N}_{0})$, for $\nu\in\mathbb{R}$, $\nu\neq0,-1,-2,\dots$. The…

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known…

Let $\mathcal{A}$ be a weakly irreducible nonnegative tensor with spectral radius $\rho(\mathcal{A})$. Let $\mathfrak{D}$ (respectively, $\mathfrak{D}^{(0)}$) be the set of normalized diagonal matrices arising from the eigenvectors of…

We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by $ 2 \*\sigma + o(N^{-6/11+\epsilon}), $ where $\sigma^2 $ is the…

In this paper, we introduce a new type of parallelism for bounded linear operators on a Hilbert space $\big(\mathscr{H}, \langle \cdot ,\cdot \rangle\big)$ based on numerical radius. More precisely, we consider operators $T$ and $S$ which…

We study the spectrum of 4-cycle row-stochastic matrices. For real eigenvalues the spectral region is [-1,1]. For nonreal eigenvalues a+ib we derive necessary conditions in terms of the real and imaginary parts, including the inequality…

Let $B(H)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space $H$. For $T \in B(H)$ and $\lambda \in \mathbb{C}$, let $H_{T}(\{\lambda\})$ denotes the local spectral subspace of $T$ associated…

Let $z_1, \cdots, z_p$ be the eigenvalues of $A,$ which is the left-top $p\times p$ submatrix of an $n\times n$ Haar-invariant unitary matrix. Suppose there exist two constants $0<h_1<h_2<1$ such that $h_1<\frac pn<h_2.$ Then, $$\sup_{x\in…