A Radon–Nikodým theorem for local completely positive invariant multilinear maps
Linear and Multilinear Algebra
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.
Ghatak, Anindya and Pamula, Santhosh Kumar, "A Radon–Nikodým theorem for local completely positive invariant multilinear maps" (2021). Journal Articles. 2159.