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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 10, Pages 18–30 (Mi ivm7136)  
This article is cited in 2 scientific papers (total in 2 papers)

Noncommutative integration for traces with values in Kantorovich–Pinsker spaces

B. S. Zakirova, V. I. Chilinb

a Chair of Higher Mathematics, Tashkent Railway Engineering Institute, Tashkent, Republic of Uzbekistan
b Chair of Algebra and Function Analysis, National University of Uzbekistan, Tashkent, Republic of Uzbekistan
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Abstract: In this paper we consider traces on von Neumann algebras with values in complex Kantorovich–Pinsker spaces. We establish the connection between the convergence with respect to the trace and the convergence locally in measure in the algebra $S(M)$ of measurable operators affiliated with $M$. We define the $(bo)$-complete lattice-normed spaces of integrable operators in $S(M)$ and prove that they are decomposable if the trace possesses the Maharam property.
Keywords: von Neumann algebra, measurable operator, convergence locally in measure, vector-valued trace, Banach–Kantorovich space.
Received: 21.01.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 10, Pages 15–26
DOI: https://doi.org/10.3103/S1066369X10100026
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: B. S. Zakirov, V. I. Chilin, “Noncommutative integration for traces with values in Kantorovich–Pinsker spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 10, 18–30; Russian Math. (Iz. VUZ), 54:10 (2010), 15–26
Citation in format AMSBIB
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\by B.~S.~Zakirov, V.~I.~Chilin
\paper Noncommutative integration for traces with values in Kantorovich--Pinsker spaces
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 10
\pages 18--30
\mathnet{http://mi.mathnet.ru/ivm7136}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2808738}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 10
\pages 15--26
\crossref{https://doi.org/10.3103/S1066369X10100026}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649585311}
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    • This publication is cited in the following 2 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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