Related papers: Tolerance relations and operator systems

The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation property, and thus that norms of operators…

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed…

The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…

Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite…

This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…

Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…

In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in…

(This short article is a continuation of a longer, review work, in the same volume of Proceedings, by Ashtekar, Marolf and Mour\~ao [gr-qc/9403042]. All the details and other results are to be found in joint papers of the author with Abhay…

We consider planar noncommutative theories such that the coordinates verify a space-dependent commutation relation. We show that, in some special cases, new coordinates may be introduced that have a constant commutator, and as a consequence…

We give some new characterizations of unitaries, isometries, unital operator spaces, unital function spaces, operator systems, C*-algebras, and related objects. These characterizations only employ the vector space and operator space…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=…

This is a continuation of the paper (quant-ph/0009012). In this letter we extend coherent operators and study some basic properties (the disentangling formula, resolution of unity, commutation relation, etc). We also propose a perspective…

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…

We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…

We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…

Consider an infinite-dimensional linear space equipped with a Gaussian measure and the group $GL(\infty)$ of linear transformations that send the measure to equivalent one. Limit points of $GL(\infty)$ can be regarded as 'spreading' maps…

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian…

We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…