Quotients of quantum bornological spaces
type: Item
instance of: scholarly article
title: Quotients of quantum bornological spaces
zbMATH Open document ID: 1244.47060
published in: Taiwanese Journal of Mathematics
publication date: 2011-12-19T00:00:00Z
review text: The duality theory for operator spaces consists of two main results. One is that for an operator space \(X \subset V\), the restriction \(\phi: V^* \to X^*\) defined by \(\phi(f)=f|_X\) is an exact matrix quotient mapping. The other is that any complete operator space is a matrix quotient of an \(L^1\)-direct sum of finite-dimensional trace class algebras up to a matrix isometry. These properties play key roles in tensor products of operator spaces. In this paper, the author investigates the duality for quantum spaces equipped with quantum bornologies. Particularly, it is shown that a finite complete bornology admits one unique quantization and any complete quantum space is a matrix bornology quotient of a local trace class algebra.
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 47L25
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46A17
zbMATH DE Number: 5989939
zbMATH Keywords: quantum bornological spaces
zbMATH Keywords: absolutely matrix convex set
zbMATH Keywords: matrix seminorm
zbMATH Keywords: Hilbert-Schmidt boundary
zbMATH Keywords: exact matrix quotient mapping
author: Anar Dosi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406300
OpenAlex ID: W1552444109
DOI: 10.11650/TWJM/1500406300
description: scientific article; zbMATH DE number 5989939