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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm8469https://doi.org/10.4213/mzm8469 https://www.mathnet.ru/eng/mzm/v87/i4/p502
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Abstract page: | 496 | Full-text PDF : | 189 | References: | 55 | First page: | 9 |
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