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The Russo-Dye Theorem in Nest Algebras
Author(s):
Kenneth
R.
Davidson
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3055-3059.
MSC (1991):
Primary 47D25
MathSciNet review:
1468188
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Abstract:
It is shown that the convex hull of the unitary elements of a nest algebra contains the whole unit ball if and only if both  and  are either zero or infinite rank.
References:
- 1.
- M. Anoussis and E. Katsoulis, A nonself-adjoint Russo-Dye Theorem, Math. Ann. 304, (1996), 685-699. MR 97f:47042
- 2.
- K.R. Davidson, Nest Algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific and Technical Pub. Co., London, New York, 1988. MR 90f:47062
- 3.
- R.V. Kadison and G.K. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 245-266. MR 87g:47078
- 4.
- D.R. Larson, Nest algebras and similarity transformations, Ann. Math. 121 (1985), 409-427. MR 86j:47061
- 5.
- R. Moore and T. Trent, Extreme points of certain operator algebras, Indiana U. Math. J. 36 (1987), 645-650. MR 89d:47103
- 6.
- B. Russo and H. Dye, A note on unitary operators in C*-algebras, Duke Math. J. 33 (1966), 413-416. MR 33:1750
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Additional Information:
Kenneth
R.
Davidson
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email:
krdavidson@math.uwaterloo.ca
DOI:
10.1090/S0002-9939-98-04538-9
PII:
S 0002-9939(98)04538-9
Received by editor(s):
March 17, 1997
Additional Notes:
The author was partially supported by an NSERC grant and a Killam Research Fellowship.
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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