Related papers: Von Neumann's inequality for tensors

We consider banded block Toeplitz matrices $T_n$ with $n$ block rows and columns. We show that under certain technical assumptions, the normalized eigenvalue counting measure of $T_n$ for $n\to\infty$ weakly converges to one component of…

The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.

In this article, we investigate the ball version of von Neumann inequality for the class of doubly contractive $d$-tuple of weighted shift. We show that if the weighted shift is balanced or satisfies an appropriate weight condition, then it…

The tensor t-product, introduced by Kilmer and Martin [26], is a powerful tool for the analysis of and computation with third-order tensors. This paper introduces eigentubes and eigenslices of third-order tensors under the t-product. The…

For nonautonomous linear differential equations with nonuniform hyperbolicity, we introduce a definition for nonuniform dichotomy spectrum, which can be seen as a generalization of Sacker-Sell spectrum. We prove a spectral theorem and use…

Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metric and the product structure.

We extract a precise internal description of the sequential commutation equivalence relation introduced in [KEP23] for tracial von Neumann algebras. As an application we prove that if a tracial von Neumann algebra $N$ is generated by…

This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative…

We prove an infinite sequence of inequalities among scalar polynomial invariants of symmetric rank-2 tensors of Segre types $A1$, $A3$, and $B$. In particular, these inequalities apply to the Ricci tensor and the energy-momentum tensor. If…

In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and…

Let $\M$ be a von Neumann algebra acting on a Hilbert space $\H$, and $\N$ be a singular von Neumann subalgebra of $\M.$ If $\N\tensor\B(\K)$ is singular in $\M\tensor\B(\K)$ for any Hilbert space $\K$, we say $\N$ is \emph{completely…

We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many…

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…

In a 1918 paper Schur proved a remarkable inequality that related group representations, Hermitian forms and determinants. He also gave concise necessary and sufficient conditions for equality. In 1964, Marcus gave a beautiful short proof…

We prove a theorem on scalar-valued functions of tensors, where ``scalar'' refers to absolute scalars as well as relative scalars of weight $w$. The present work thereby generalizes an identity referred to earlier by Rosenfeld in his…

A famous theorem due to Weyl and von Neumann asserts that two bounded self-adjoint operators are unitarily equivalent modulo the compacts, if and only if their essential spectrum agree. The above theorem does not hold for unbounded…

Let $\Gamma$ be a discrete group acting on a compact Hausdorff space $X$. Given $x\in X$, and $\mu\in\text{Prob}(X)$, we introduce the notion of contraction of $\mu$ towards $x$ with respect to unitary elements of a group von Neumann…

We study the spectrum of the product of two Toeplitz operators. Assume that the symbols of these operators are continuous and real-valued and that one of them is non-negative. We prove that the spectrum of the product of finite section…

Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.

The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…