Related papers: Operator Positivstellens\"atze for noncommutative …

We generalize the first part of A. Connes paper (math/9811068) on the zeroes of the Riemann zeta function from a number field $k$ to any simple algebra $M$ over $k$. To a given automorphic representation $\pi$ of the reductive group…

In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries…

Given a non-zero polynomial $P(x)$, we study Fuchsian differential operators of the form $L=\partial_x^2-u(x)$ such that for all $\lambda\in\mathbb{C}$ the operator $L+\lambda P(x)$ is monodromy free. We prove that all such operators are…

Recently, non-SOS Positivstellens\"atze for polynomials on compact semialgebraic sets, following the general form of Schm\"{u}dgen's Positivstellensatz, have been derived by appropriately replacing the SOS polynomials with other classes of…

A spectrahedron is the positivity region of a linear matrix pencil and thus the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in…

The purpose of this note is to provide a family of explicit examples of $4$-dimensional operator systems contained in the Calkin algebra $\mathcal{Q}(\mathcal{H})$ on a separable infinite-dimensional Hilbert space $\mathcal{H}$ for which…

A Positive Operator Valued Measure (POVM) is a map $F:\mathcal{B}(X)\to\mathcal{L}_s^+(\mathcal{H})$ from the Borel $\sigma$-algebra of a topological space $X$ to the space of positive self-adjoint operators on a Hilbert space…

Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…

We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…

The main goal of this dissertation is to find conditions which will guarantee the existence of solutions in the Hilbert space $H$ of semilinear equation \[ L u+N(u)=h \] where $L$ is a linear and self-adjoint operator, $N$ a non-linear…

We generalise the Riesz representation theorems for positive linear functionals on $\mathrm{C}_{\mathrm c}(X)$ and $\mathrm{C}_{\mathrm 0}(X)$, where $X$ is a locally compact Hausdorff space, to positive linear operators from these spaces…

For linear operators $L, T$ and nonlinear maps $P$, we describe classes of simple maps $F = I - P T$, $F = L - P$ between Banach and Hilbert spaces, for which no point has more than two preimages. The classes encompass known examples…

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…

This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…

Given a general symmetric elliptic operator $$ L\_{a} := \sum\_{k,,j=1}^d \p\_k (a\_{kj} \p\_j) + \sum\_{k=1}^d a\_k \p\_k - \p\_k(\overline{a\_k} .) + a\_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with partial data,…

Let $(M,g)$ be a complete non-compact Riemannian manifold. We consider operators of the form $\Delta_g + V$, where $\Delta_g$ is the non-negative Laplacian associated with the metric $g$, and $V$ a locally integrable function. Let $\rho :…

Three linear operators (${\mathcal L}$-operators) determining automorphisms of the space of solutions to a special double confluent Heun equation (sDCHE) of negative integer order are considered. Their composition rules involving in a…

We establish two global subellipticity properties of positive symmetric second-order partial differential operators on $L_2(\Ri^d)$. First, if $m \in \Ni$ then we consider operators $H_0$ with coefficients in $W^{m+1,\infty}(\Ri^d)$ and…

We revisit the problem of property testing for convex position for point sets in $\mathbb{R}^d$. Our results draw from previous ideas of Czumaj, Sohler, and Ziegler (ESA 2000). First, the algorithm is redesigned and its analysis is revised…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…