The commutant of L(H) in its ultrapower may or may not be trivial

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The Commutant of L(h) in Its Ultrapower May or May Not Be Trivial

Kirchberg asked in 2004 whether the commutant of L(H) in its (norm) ultrapower is trivial. Assuming the Continnuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter. Let H be a separable infinite dimensional complex Hilbert space, fixed throughout. The purpose of this paper is to prove that, assuming the Continnuum Hypothesis, the commutant of L(H) (the algebra of bo...

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ژورنال

عنوان ژورنال: Mathematische Annalen

سال: 2009

ISSN: 0025-5831,1432-1807

DOI: 10.1007/s00208-009-0448-z