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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 502–513
DOI: https://doi.org/10.4213/mzm8469
(Mi mzm8469)
 

This article is cited in 4 scientific papers (total in 4 papers)

Notes on Derivations on Algebras of Measurable Operators

A. F. Bera, B. de Pagterb, F. A. Sukochevc

a ISV "Solutions"
b Delft University of Technology
c University of New South Wales
Full-text PDF (505 kB) Citations (4)
References:
Abstract: Derivations on algebras of (unbounded) operators affiliated with a von Neumann algebra $\mathscr M$ are considered. Let $\mathscr A$ be one of the algebras of measurable operators, of locally measurable operators, and of $\tau$-measurable operators. The von Neumann algebras $\mathscr M$ of type I for which any derivation on $\mathscr A$ is inner are completely described in terms of properties of central projections. It is also shown that any derivation on the algebra $LS(\mathscr M)$ of all locally measurable operators affiliated with a properly infinite von Neumann algebra $\mathscr M$ vanishes on the center $LS(\mathscr M)$.
Keywords: operator algebra, von Neumann algebra, measurable operator algebra, derivation on an operator algebra, inner derivation, bimodule, $*$-algebra.
Received: 08.07.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 475–484
DOI: https://doi.org/10.1134/S0001434610030259
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
Citation: A. F. Ber, B. De Pagter, F. A. Sukochev, “Notes on Derivations on Algebras of Measurable Operators”, Mat. Zametki, 87:4 (2010), 502–513; Math. Notes, 87:4 (2010), 475–484
Citation in format AMSBIB
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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