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ISSN 1088-6826(e) ISSN 0002-9939(p)

Extreme points of weakly closed $\mathcal{T(N)}$ -modules

Author(s): Dong Zhe; Lu Shijie
Journal: Proc. Amer. Math. Soc. 130 (2002), 461-469.
MSC (2000): Primary 47L75
Posted: July 25, 2001
MathSciNet review: 1862126
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Abstract: In this paper, we first characterize the rank one operators in the preannihilator $\mathcal{U}_{\bot}$ of a weakly closed $\mathcal{T(N)}$ -module $\mathcal{U}$ . Using this characterization for the rank one operators in $\mathcal{U}_{\bot}$ , a complete description of the extreme points of the unit ball $\mathcal{U}_{1}$ is given. Finally, we show how to apply the techniques of the present paper to other operator systems and characterize their extreme points.

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Additional Information:

Dong Zhe
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China
Address at time of publication: Institute of Mathematics, Fudan University, Shanghai 200433, People's Republic of China
Email: dzhe8@china.com

Lu Shijie
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China

DOI: 10.1090/S0002-9939-01-06075-0
PII: S 0002-9939(01)06075-0
Keywords: Weakly closed $\mathcal{ T(N)}$--module, preannihilator, extreme point, contractive perturbation
Received by editor(s): November 15, 1999
Received by editor(s) in revised form: June 26, 2000
Posted: July 25, 2001
Additional Notes: This work was supported by the National Natural Science Foundation of China.
Communicated by: David R. Larson
Copyright of article: Copyright 2001, American Mathematical Society

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