Completely positive maps on Hilbert modules over pro-C*-algebras

2016/11/15 by Khadijeh Karimi, Karimi, Khadijeh, Kamran Sharifi +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.OA #msc:46K10 #msc:46L05 #msc:46L08

paper · pdf · doi:10.48550/arxiv.1611.04759

15 pages, accepted. arXiv admin note: text overlap with arXiv:1611.04707

arxiv created 2016/11/15 · arxiv updated 2017/01/05

Abstract

We derive Paschke's GNS construction for completely positive maps on unital pro-C*-algebras from the KSGNS construction, presented by M. Joita [J. London Math. Soc. \bf 66 (2002), 421--432], and then we deduce an analogue of Stinespring theorem for Hilbert modules over pro-C*-algebras. Also, we obtain a Radon-Nikodym type theorem for operator valued completely positive maps on Hilbert modules over pro-C*-algebras.

Citations

• Subalgebras of C*-algebras
• Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem

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