A Radon–Nikodým theorem for completely positive invariant multilinear maps and its applications

Abstract

Link to this article: http://journals.cambridge.org/abstract_S0305004101005503How to cite this article: JAESEONG HEO (2002). A Radon-Nikodým theorem for completely positive invariant multilinear maps and its applications.

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

“…In this article, our main concern is to study the structure of k-linear local CP-maps between locally C * -algebras. These results generalize the work of Heo [16].…”

“…Finally, we show that the product of these local contractive * -homomorphisms is a desired dilation of the given invariant local completely positive k-linear map (see Theorem 3.2). This result extends the Anar Dosiev's Stinespring theorem [6, Theorem 5.1] to k-linear maps and a locally convex analogue of Heo's result [16].…”

“…In this section, we obtain Stinespring type representation for symmetric local completely contractive and local completely positive invariant k-linear maps. Our result is a locally convex analogue of Heo's work [16] as we deal with a multilinear local positive map between local C * -algebras. In particular, if k = 1 then the result coincides with [6, Theorem 5.1].…”

“…Note that if k = 1, then Definitions 2.4, 2.5 coincide with the notion of local completely contractive and local completely positive linear maps defined between local C * -algebras [6]. Furthermore, if , are C * -algebras, then Definitions 2.4, 2.5 coincide with the notion of completely contractive and completely positive k-linear maps studied in [15,16]. Now we introduce the notion of invariance from [16] to k-linear maps on locally C * -algebras.…”

“…Furthermore, if , are C * -algebras, then Definitions 2.4, 2.5 coincide with the notion of completely contractive and completely positive k-linear maps studied in [15,16]. Now we introduce the notion of invariance from [16] to k-linear maps on locally C * -algebras.…”