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On Voiculescu's double commutant theorem |
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| Authors: | C. A. Berger L. A. Coburn |
| Affiliation: | Department of Mathematics and Computer Science, Herbert H. Lehman College, City University of New York, Bronx, New York 10468 L. A. Coburn ; Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214 |
| 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
In this note, we exhibit a non-separable unital |
| Keywords: | |
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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 
, 
-subalgebra 
of 
for which (VDCT) fails.