A. F. Ber, “Continuous Derivations on $*$-Algebras of $\tau$-Measurable Operators Are Inner”, Mat. Zametki, 93:5 (2013), 658–664; Math. Notes, 93:5 (2013), 654

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Matematicheskie Zametki, 2013, Volume 93, Issue 5, Pages 658–664
DOI: https://doi.org/10.4213/mzm10231 (Mi mzm10231)

This article is cited in 5 scientific papers (total in 5 papers)

Continuous Derivations on

*

$*$ -Algebras of

$\tau$ -Measurable Operators Are Inner

A. F. Ber

DCF Technologies Ltd.

Full-text PDF (425 kB) Citations (5)

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DOI: https://doi.org/10.4213/mzm10231

Abstract: It is proved that every continuous derivation on the

$*$ -algebra

$S(\mathcal{M},\tau)$ of all

$\tau$ -measurable operators affiliated with a von Neumann algebra

$\mathcal{M}$ is inner. For every properly infinite von Neumann algebra

$\mathcal{M}$ , any derivation on the

$*$ -algebra

$S(\mathcal{M},\tau)$ is inner.

Keywords: von Neumann algebra, properly infinite,

$\tau$ -measurable operator, continuous derivation.

Received: 14.12.2012

English version:
Mathematical Notes, 2013, Volume 93, Issue 5, Pages 654–659
DOI: https://doi.org/10.1134/S0001434613050027

Bibliographic databases:

Document Type: Article

UDC: 517.98

Language: Russian

Citation: A. F. Ber, “Continuous Derivations on

$*$ -Algebras of

$\tau$ -Measurable Operators Are Inner”, Mat. Zametki, 93:5 (2013), 658–664; Math. Notes, 93:5 (2013), 654–659

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm10231

https://doi.org/10.4213/mzm10231

https://www.mathnet.ru/eng/mzm/v93/i5/p658

This publication is cited in the following 5 articles:

Aleksey Ber, Karimbergen Kudaybergenov, Fedor Sukochev, “Derivations of Murray–von Neumann algebras”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2022:791 (2022), 283
A. F. Ber, K. K. Kudaybergenov, F. A. Sukochev, “Derivations on Murray–von Neumann algebras”, Russian Math. Surveys, 74:5 (2019), 950–952
Mukhamedov F., Kudaybergenov K., “Local Derivations on Subalgebras of Tau-Measurable Operators With Respect To Semi-Finite Von Neumann Algebras”, Mediterr. J. Math., 12:3 (2015), 1009–1017
A. F. Ber, V. I. Chilin, F. A. Sukochev, “Continuous derivations on algebras of locally measurable operators are inner”, Proc. London Math. Soc., 109:1 (2014), 65–89
Sh. Ayupov, K. Kudaybergenov, “Spatiality of derivations on the algebra of $\tau$-compact operators”, Integral Equations Operator Theory, 77:4 (2013), 581–598

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

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Full-text PDF :	194
References:	70
First page:	14

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