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The commutant of $L(H)$ in its ultrapower may or may not be trivial. (English) Zbl 1200.46049
Summary: {\it 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.

46L05General theory of $C^*$-algebras
03E50Continuum hypothesis; Martin’s axiom (logic)
Full Text: DOI
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