A Radon–Nikodým theorem for local completely positive invariant multilinear maps

Authors

Anindya Ghatak, Indian Statistical Institute Bangalore
Santhosh Kumar Pamula, Birla Institute of Technology and Science, Pilani

Article Type

Research Article

Publication Title

Linear and Multilinear Algebra

Abstract

In this article, we introduce local completely positive k-linear maps between locally (Formula presented.) -algebras and obtain Stinespring type representation by adopting the notion of ‘invariance’ defined by J. Heo for k-linear maps between (Formula presented.) -algebras. Also, we supply the minimality condition to make certain that minimal representation is unique up to unitary equivalence. As a consequence, we prove Radon–Nikodým theorem for unbounded operator-valued local completely positive invariant k-linear maps. The obtained Radon–Nikodým derivative is a positive contraction on some Hilbert space with several reducing subspaces.

DOI

10.1080/03081087.2021.1983511

Publication Date

1-1-2021

Comments

Open Access, Green

Recommended Citation

Ghatak, Anindya and Pamula, Santhosh Kumar, "A Radon–Nikodým theorem for local completely positive invariant multilinear maps" (2021). Journal Articles. 2159.
https://digitalcommons.isical.ac.in/journal-articles/2159