Related papers: Classifications of linear operators preserving ell…

Let $A_{i}\ (i=1, 2, ..., k)$ be bounded linear operators on a Hilbert space. This paper aims to show characterizations of operator order $A_{k}\geq A_{k-1}\geq...\geq A_{2}\geq A_{1}>0$ in terms of operator inequalities. Afterwards, an…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

Volume polynomials measure the growth of Minkowski sums of convex bodies and of tensor powers of positive line bundles on projective varieties. We show that Aluffi's covolume polynomials are precisely the polynomial differential operators…

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or corank, here we consider the problem inbetween, that is, we treat the question of preserving operators…

We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…

In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…

We consider divergence form elliptic operators $L=-\dv A(x)\nabla$, defined in $\mathbb{R}^{n+1}=\{(x,t)\in\mathbb{R}^{n}\times\mathbb{R}\}, n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic,…

Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…

Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided Polya frequency functions, or totally positive kernels are treated from a unifying perspective. Besides the stark rigidity of the polynomial…

In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis,…

Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed…

Let $ \mathcal D$ be a dense linear manifold in a Hilbert space $\mathcal H$ and let $L^+(\mathcal D)$ be the *-algebra of all linear operators $A$ such that $A \mathcal D \subset \mathcal D, A^* \mathcal D \subset \mathcal D$. Denote by…

The solutions of the equation $f^{(p-1)} + f^p = h^p$ in the unknown function $f $over an algebraic function field of characteristic $p$ are very closely linked to the structure and factorisations of linear differential operators with…

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…

The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of…

We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…

For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is…

The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…

We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only if the norms of its powers grow polynomially. In analogy with unitary dilations of contractions, we prove that such…

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…