Stinespring's theorem for unbounded operator valued local completely positive maps and its applications

Authors

B. V.Rajarama Bhat, Indian Statistical Institute Bangalore
Anindya Ghatak, Indian Statistical Institute Bangalore
Santhosh Kumar Pamula, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Indagationes Mathematicae

Abstract

Dosiev (2008) obtained a Stinespring's theorem for local completely positive maps (in short: local CP-maps) on locally C∗-algebras. In this article a suitable notion of minimality for this construction has been identified so as to ensure uniqueness up to unitary equivalence for the associated representation. Using this a Radon–Nikodym type theorem for local completely positive maps has been proved. Further, a Stinespring's theorem for unbounded operator valued local completely positive maps on Hilbert modules over locally C∗-algebras (also called as local CP-inducing maps) has been presented. Following a construction of M. Joiţa, a Radon–Nikodym type theorem for local CP-inducing maps has been shown. In both cases the Radon–Nikodym derivative obtained is a positive contraction on some complex Hilbert space with an upward filtered family of reducing subspaces.

First Page

547

Last Page

578

DOI

10.1016/j.indag.2021.01.001

Publication Date

4-1-2021

Comments

Open Access, Green

Recommended Citation

Bhat, B. V.Rajarama; Ghatak, Anindya; and Pamula, Santhosh Kumar, "Stinespring's theorem for unbounded operator valued local completely positive maps and its applications" (2021). Journal Articles. 2020.
https://digitalcommons.isical.ac.in/journal-articles/2020