The Russo-Dye Theorem in a weakly closed -module

Author:
Zhe Dong

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2257-2263

MSC (2000):
Primary 47L75

DOI:
https://doi.org/10.1090/S0002-9939-04-07141-2

Published electronically:
March 25, 2004

MathSciNet review:
2052401

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that is admissible. It is shown that the convex hull of unitary elements of a weakly closed -module contains the whole unit ball of if and only if and for any , .

**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, The Russo-Dye theorem in nest algebras, Proc. Amer. Math. Soc. 126 (1998), 3055-3059. MR**2000f:47109****3.**Dong Zhe and Lu Shijie, Extreme points of weakly closed -modules, Proc. Amer. Math. Soc. 130 (2002), 461-469. MR**2002m:47086****4.**J.A.Erdos and S.C.Power, Weakly closed ideals of nest algebras, J. Operator Theory 7 (1982), 219-235. MR**84a:47056****5.**R.V.Kadison and G.K.Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 245-266. MR**87g:47078****6.**D.R.Larson, Nest algebras and similarity transforms, Ann. Math. 121 (1985), 409-427. MR**86j:47061****7.**R.Moore and T.Trent, Extreme points of certain operator algebras, Indiana U. Math. J. 36 (1987), 645-650. MR**89d:47103****8.**B.Russo and H.Dye, A note on unitary operators in -algebras, Duke Math. J. 33 (1966), 413-416. MR**33:1750**

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Additional Information

**Zhe Dong**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Email:
dongzhe@zju.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-04-07141-2

Keywords:
Russo-Dye Theorem,
weakly closed $\mathcal{T(N)} $--module,
unitary operator

Received by editor(s):
October 19, 2000

Published electronically:
March 25, 2004

Communicated by:
David R. Larson

Article copyright:
© Copyright 2004
American Mathematical Society