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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 1, Pages 77–79 (Mi faa3099)  

Brief communications

Commutator Estimates in von Neumann Algebras

A. F. Bera, F. A. Sukochevb

a DCF Technologies Ltd.
b University of New South Wales, School of Mathematics and Statistics

Abstract: Let $\mathcal{M}$ be a von Neumann algebra. For every self-adjoint locally measurable operator $a$, there exists a central self-adjoint locally measurable operator $c_0$ such that, given any $\varepsilon>0$, $|[a,u_\varepsilon]|\ge(1-\varepsilon)|a-c_0|$ for some unitary operator $u_\varepsilon\in\mathcal{M}$. In particular, every derivation $\delta\colon\mathcal{M}\to\mathcal{I}$ (where $\mathcal{I}$ is an ideal in $\mathcal{M}$) is inner, and $\delta=\delta_a$ for $a\in\mathcal{I}$.

Keywords: derivation, von Neumann algebra, measurable operator, symmetric operator ideal

DOI: https://doi.org/10.4213/faa3099

Full text: PDF file (141 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:1, 62–63

Bibliographic databases:

UDC: 517.98
Received: 03.02.2011

Citation: A. F. Ber, F. A. Sukochev, “Commutator Estimates in von Neumann Algebras”, Funktsional. Anal. i Prilozhen., 47:1 (2013), 77–79; Funct. Anal. Appl., 47:1 (2013), 62–63

Citation in format AMSBIB
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