Operator valued probability theory
type: Item
instance of: scholarly article
title: Operator valued probability theory
zbMATH Open document ID: 1057.60008
author: P. Jakobsen
author: Valentin Lychagin
published in: Lobachevskii Journal of Mathematics
publication date: 2004-11-26T00:00:00Z
full work available at URL: https://eudml.org/doc/232112
full work available at URL: jcl.html
review text: In the first four sections an extended probability theory is developed. In the following two sections the corresponding category of extended probability spaces is introduced and basic categorical constructions corresponding to fundamental probability notions are described. An extended probability space consists of the Borel sets \(B(X)\) of a second countable locally compact Hausdorff topological space \(X\) and a suitable (sequentially continuous positive normed) operator valued measure \(F\) on \(B(X)\) into the real \(C^*\) algebra \(O(H)\) of bounded operators on the real Hilbert space \(H\). Besides other generalizations of probability notions, the authors have developed a notion of probability density for operator valued measures as an element in a Hilbert module. In the last section, products, dependence and independence are shown to be related to the monoidal structure of the category of extended probability spaces.
reviewed by: Roman Frič
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 46N30
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 2119181
zbMATH Keywords: extended probability space
zbMATH Keywords: operator valued measure
zbMATH Keywords: half density
zbMATH Keywords: category of extended probability spaces
zbMATH Keywords: monoidal category
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2119181