Measure continuous derivations on von Neumann algebras and applications to L2-cohomology

David Kyed, Vadim Alekseev

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

We prove that norm continuous derivations from a von Neumann algebra into the algebra of operators affiliated with its tensor square are automatically continuous for both the strong operator topology and the measure topology. Furthermore, we prove that the first continuous L2-Betti number scales quadratically when passing to corner algebras and derive an upper bound given by Shen's generator invariant. This, in turn, yields vanishing of the first continuous L2-Betti number for \twoone factors with property (T), for finitely generated factors with non-trivial fundamental group and for factors with property Gamma.
OriginalsprogEngelsk
TidsskriftJournal of Operator Theory
Vol/bind73
Udgave nummer1
Sider (fra-til)91-111
ISSN0379-4024
DOI
StatusUdgivet - 1. jan. 2015

Fingeraftryk

Von Neumann Algebra
Cohomology
Betti numbers
Strong Operator Topology
Algebra
Fundamental Group
Finitely Generated
Tensor
Generator
Upper bound
Topology
Norm
Invariant
Operator

Citer dette

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Measure continuous derivations on von Neumann algebras and applications to L2-cohomology. / Kyed, David; Alekseev, Vadim.

I: Journal of Operator Theory, Bind 73, Nr. 1, 01.01.2015, s. 91-111.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Measure continuous derivations on von Neumann algebras and applications to L2-cohomology

AU - Kyed, David

AU - Alekseev, Vadim

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Y1 - 2015/1/1

N2 - We prove that norm continuous derivations from a von Neumann algebra into the algebra of operators affiliated with its tensor square are automatically continuous for both the strong operator topology and the measure topology. Furthermore, we prove that the first continuous L2-Betti number scales quadratically when passing to corner algebras and derive an upper bound given by Shen's generator invariant. This, in turn, yields vanishing of the first continuous L2-Betti number for \twoone factors with property (T), for finitely generated factors with non-trivial fundamental group and for factors with property Gamma.

AB - We prove that norm continuous derivations from a von Neumann algebra into the algebra of operators affiliated with its tensor square are automatically continuous for both the strong operator topology and the measure topology. Furthermore, we prove that the first continuous L2-Betti number scales quadratically when passing to corner algebras and derive an upper bound given by Shen's generator invariant. This, in turn, yields vanishing of the first continuous L2-Betti number for \twoone factors with property (T), for finitely generated factors with non-trivial fundamental group and for factors with property Gamma.

UR - http://www.mathjournals.org/jot/2015-073-001/

UR - https://arxiv.org/abs/1110.6155

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DO - 10.7900/jot.2013sep23.2018

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JO - Journal of Operator Theory

JF - Journal of Operator Theory

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