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

Article Type

Research Article

Publication Title

Linear and Multilinear Algebra

Abstract

In this article, we introduce local completely positive k-linear maps between locally C*-algebras and obtain Stinespring type representation by adopting the notion of ‘invariance’ defined by J. Heo for k-linear maps between C*-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.

First Page

7115

Last Page

7141

DOI

10.1080/03081087.2021.1983511

Publication Date

1-1-2022

Comments

Open Access, Green

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