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Proceedings of the American Mathematical Society

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


Authors: Dong Zhe and Lu Shijie
Journal: Proc. Amer. Math. Soc. 130 (2002), 461-469
MSC (2000): Primary 47L75
DOI: https://doi.org/10.1090/S0002-9939-01-06075-0
Published electronically: 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: 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