Extreme points of weakly closed -modules

Authors:
Dong Zhe and Lu Shijie

Journal:
Proc. Amer. Math. Soc. **130** (2002), 461-469

MSC (2000):
Primary 47L75

Published electronically:
July 25, 2001

MathSciNet review:
1862126

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we first characterize the rank one operators in the preannihilator of a weakly closed -module . Using this characterization for the rank one operators in , a complete description of the extreme points of the unit ball 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:
https://doi.org/10.1090/S0002-9939-01-06075-0

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

Published electronically:
July 25, 2001

Additional Notes:
This work was supported by the National Natural Science Foundation of China.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society