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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 12, Pages 50–59 (Mi ivm9419)  
This article is cited in 1 scientific paper (total in 1 paper)

Modular sesquilinear forms and generalized Stinspring representation

A. V. Kalinichenkoa, I. N. Malievb, M. A. Plievc

a North-Caucasian Institute of Mining and Metallurgy named after K.L. Khetagurov, (State Technological University), 44 Nikolaeva str., Vladikavkaz, 362021 Russia
b North-Ossetian State University, 44–46 Vatutina str., Vladikavkaz, 362025 Russia
c Southern Mathematical Institute, the Vladikavkaz Scientific Center of the Russian Academy of Sciences, 22 Markusa str., Vladikavkaz, 362027 Russia
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Abstract: We consider completely positive maps defined on locally $C^{\ast}$-algebra and taking values in the space of sesquilinear forms on Hilbert $C^{\ast}$-module $\mathcal{M}$. We construct the Stinspring type representation for this type of maps and show that any two minimal Stinspring representations are unitarily equivalent.
Keywords: Hilbert $C^\ast$-module, locally $C^{\ast}$-algebra, sesquilinear form, completely positive map, $\ast$-homomorphism, positive definite kernel, Stinspring's representation.
Funding agency Grant number
Russian Foundation for Basic Research 17-51-12064_ННИО_а
Received: 08.11.2017
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 12, Pages 42–49
DOI: https://doi.org/10.3103/S1066369X18120034
Bibliographic databases:
Document Type: Article
UDC: 517.983:517.986
Language: Russian
Citation: A. V. Kalinichenko, I. N. Maliev, M. A. Pliev, “Modular sesquilinear forms and generalized Stinspring representation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 12, 50–59; Russian Math. (Iz. VUZ), 62:12 (2018), 42–49
Citation in format AMSBIB
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\by A.~V.~Kalinichenko, I.~N.~Maliev, M.~A.~Pliev
\paper Modular sesquilinear forms and generalized Stinspring representation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 12
\pages 50--59
\mathnet{http://mi.mathnet.ru/ivm9419}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 12
\pages 42--49
\crossref{https://doi.org/10.3103/S1066369X18120034}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85058480443}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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