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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.7 P.759-763

http://doi.org/10.1631/jzus.2004.0759


Extreme points of norm closed nest algebra modules


Author(s):  DONG Zhe

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   dongzhe@zju.edu.cn

Key Words:  Extreme point, Nest algebra module, Rank one operator


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DONG Zhe. Extreme points of norm closed nest algebra modules[J]. Journal of Zhejiang University Science A, 2004, 5(7): 759-763.

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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2004.0759"
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Abstract: 
Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U, a complete description of the extreme points of the unit ball U1 is given.

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Reference

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[3] Arazy, J., Solel, B., 1990. Isometries of non self-adjoint operator algebras.J. Funct. Anal.,90:284-305.

[4] Davidson, K.R., 1998. The Russo-Dye theorem in nest algebras.Proc. Amer. Math. Soc.,126(10):3055-3059.

[5] Dong, Z., Lu, S.J., 2002. Extreme points of weakly closed Alg(N)-modules.Proc. Amer. Math. Soc.,130:461-469.

[6] Erdos, J.A., Power, S.C., 1982. Weakly closed ideals of nest algebras.J. Operator Theory,7:219-235.

[7] Hudson, T.D., Katsoulis, E.G., Larson, D.R., 1997. Extreme points in triangular UHF algebras.Trans. Amer. Math. Soc.,349:3391-3400.

[8] Kadison, R.V., 1951. Isometries of operator algebras.Ann. of Math.,54(2):325-38.

[9] Moore, R.L., Trent, T.T., 1987. Extreme points of certain operator algebras.Indiana U. Math. J.,36:645-50.

[10] Moore, R.L., Trent, T.T., 1989. Isometries of nest algebras.J. Funct. Anal.,86:180-209.

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