Related papers: Orthogonal Pure States in Operator Theory
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total…
Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and…
Here we present a detailed account of the fundamental problems one encounters in projection theory when non-orthogonal basis sets are used for representation of the operators. In particular, we re-examine the use of projection operators in…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations which can be performed on Gaussian states using linear optical elements…
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…
We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.
We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an…
Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
This dissertation discusses some properties of topologically ordered states as they appear in the setting of infinite quantum spin systems. We begin by studying the set of infinite volume ground states for Kitaev's abelian quantum double…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…
We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a…