This article is cited in 2 papers

Modular sesquilinear forms and generalized Stinspring representation

A. V. Kalinichenko^a, I. N. Maliev^b, M. A. Pliev<sup>c

a</sup> 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

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.

UDC: 517.983:517.986

Received: 08.11.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:12, 42–49

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