On Voiculescu's double commutant theorem
Authors:
C. A. Berger and L. A. Coburn
Journal:
Proc. Amer. Math. Soc. 124 (1996), 34533457
MSC (1991):
Primary 47L05
MathSciNet review:
1346963
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Abstract: For a separable infinitedimensional Hilbert space , we consider the full algebra of bounded linear transformations and the unique nontrivial normclosed twosided 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 nonseparable unital subalgebra of for which (VDCT) fails.
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 L. A. Coburn and J. Xia, Toeplitz algebras and Rieffel deformations, Comm. Math. Physics, 168 (1995) 2338.
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 B. E. Johnson and S. K. Parrott, Operators commuting with a von Neumann algebra modulo the set of compact operators, J. Funct. Analysis 11 (1972) 3961. MR 49:5869
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 S. Popa, The commutant modulo the set of compact operators of a von Neumann algebra, J. Funct. Analysis 71 (1987) 393408. MR 88b:46091
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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/S0002993996035319
PII:
S 00029939(96)035319
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
