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The commutant of L(H) in its ultrapower may or may not be trivial. (English) Zbl 1200.46049
Summary: E. Kirchberg [Abel Symposia 1, 175–231 (2006; Zbl 1118.46054)] asked whether the commutant of L(H) in its (norm) ultrapower is trivial. Assuming the continuum hypothesis, we prove that the answer depends on the choice of the ultrafilter.
MSC:
46L05General theory of C * -algebras
03E50Continuum hypothesis; Martin’s axiom (logic)
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