I. G. Ganiev, V. I. Chilin, “Measurable Bundles of Noncommutative $L_p$-Spaces Associated with a Center-valued Trace”, Mat. Tr., 4:2 (2001), 27–41; Siberian Adv. Math., 12:4 (2002), 19

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Matematicheskie Trudy, 2001, Volume 4, Number 2, Pages 27–41 (Mi mt11)

This article is cited in 7 scientific papers (total in 7 papers)

Measurable Bundles of Noncommutative

$L_p$ -Spaces Associated with a Center-valued Trace

I. G. Ganiev^a, V. I. Chilin^b

^a Tashkent Temir YO'L Muxandislari Instituti
^b National University of Uzbekistan named after M. Ulugbek

Full-text PDF (793 kB) Citations (7)

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Abstract: Suppose that

$M$ is a finite von Neumann algebra,

$\Phi$ is a faithful normal trace on

$M$ with values in the center of

$M$ ,

$L_p(M,\Phi)$ is the Banach–Kantorovich space of all measurable operators associated with

$M$ and

$p$ -integrable with respect to

$\Phi$ ,

$p\ge 1$ . We give a representation of

$L_p(M,\Phi)$ as a measurable bundle of noncomutative

$L_p$ -spaces associated with number traces. We also prove a “pasting” theorem for noncommutative

$L_p$ -spaces.

Key words: von Neumann algebra, center-valued trace, measurable bundle, Banach–Kantorovich space.

Received: 30.04.1999

Bibliographic databases:

UDC: 517.98

Language: Russian

Citation: I. G. Ganiev, V. I. Chilin, “Measurable Bundles of Noncommutative

$L_p$ -Spaces Associated with a Center-valued Trace”, Mat. Tr., 4:2 (2001), 27–41; Siberian Adv. Math., 12:4 (2002), 19–33

Citation in format AMSBIB

\Bibitem{GanChi01}

\by I.~G.~Ganiev, V.~I.~Chilin

\paper Measurable Bundles of Noncommutative $L_p$-Spaces Associated with a~Center-valued Trace

\jour Mat. Tr.

\yr 2001

\vol 4

\issue 2

\pages 27--41

\mathnet{http://mi.mathnet.ru/mt11}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1875507}

\zmath{https://zbmath.org/?q=an:1052.46045|1005.46030}

\transl

\jour Siberian Adv. Math.

\yr 2002

\vol 12

\issue 4

\pages 19--33

Linking options:

https://www.mathnet.ru/eng/mt11

https://www.mathnet.ru/eng/mt/v4/i2/p27

This publication is cited in the following 7 articles:

Ganiev I., Mukhamedov F., Bekbaev D., “On a Generalized Uniform Zero-Two Law For Positive Contractions of Noncommutative l-1-Spaces and Its Vector-Valued Extension”, Banach J. Math. Anal., 12:3 (2018), 600–616
Ganiev I., Mukhamedov F., “Conditional Expectations and Martingales in Noncommutative 4 l-P-Spaces Associated With Center-Valued Traces”, Acta Math. Sci., 37:4 (2017), 1019–1032
Ganiev I., Mukhamedov F., Bekbaev D., “the Strong “Zero-Two” Law For Positive Contractions of Banach-Kantorovich l-P-Lattices”, Turk. J. Math., 39:4 (2015), 583–594
Ganiev I., Mukhamedov F., “Weighted Ergodic Theorem For Contractions of Orlicz-Kantorovich Lattice l-M ((Del)Over-Cap, (Mu)Over-Cap)”, Bull. Malays. Math. Sci. Soc., 38:1 (2015), 387–397
Chilin V., Zakirov B., “Non-Commutative l-P-Spaces Associated with a Maharam Trace”, J. Operat. Theor., 68:1 (2012), 67–83
B. S. Zakirov, V. I. Chilin, “Noncommutative integration for traces with values in Kantorovich–Pinsker spaces”, Russian Math. (Iz. VUZ), 54:10 (2010), 15–26
I. G. Ganiev, K. K. Kudaibergenov, “The Banach–Steinhaus Uniform Boundedness Principle for Operators in Banach–Kantorovich Spaces over $L^0$ ”, Siberian Adv. Math., 16:3 (2006), 42–53

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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