On Voiculescu's double commutant theorem

Authors:
C. A. Berger and L. A. Coburn

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3453-3457

MSC (1991):
Primary 47L05

MathSciNet review:
1346963

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Abstract: For a separable infinite-dimensional Hilbert space , we consider the full algebra of bounded linear transformations and the unique non-trivial norm-closed two-sided ideal of compact operators . We also consider the quotient -algebra with quotient map

For any -subalgebra of , the relative commutant is given by for all in . It was shown by D. Voiculescu that, for any *separable* unital -subalgebra of ,

In this note, we exhibit a *non-separable* unital -subalgebra of for which (VDCT) fails.

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Additional Information

**C. A. Berger**

Affiliation:
Department of Mathematics and Computer Science, Herbert H. Lehman College, City University of New York, Bronx, New York 10468

**L. A. Coburn**

Affiliation:
Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214

DOI:
http://dx.doi.org/10.1090/S0002-9939-96-03531-9

Received by editor(s):
May 30, 1995

Additional Notes:
This research was partially supported by NSF grant 9500716

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society