The Russo-Dye Theorem in Nest Algebras

Author:
Kenneth R. Davidson

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3055-3059

MSC (1991):
Primary 47D25

DOI:
https://doi.org/10.1090/S0002-9939-98-04538-9

MathSciNet review:
1468188

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Abstract | References | Similar Articles | Additional Information

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.

**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**

Email:
krdavidson@math.uwaterloo.ca

DOI:
https://doi.org/10.1090/S0002-9939-98-04538-9

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

Article copyright:
© Copyright 1998
American Mathematical Society