Finite rank operators in closed maximal triangular algebras II

Authors:
Zhe Dong and Shijie Lu

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1515-1525

MSC (2000):
Primary 47L75

DOI:
https://doi.org/10.1090/S0002-9939-02-06748-5

Published electronically:
October 1, 2002

MathSciNet review:
1949882

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we discuss finite rank operators in a closed maximal triangular algebra . Based on the following result that each finite rank operator of can be written as a finite sum of rank one operators each belonging to , we proved that , where , if ; and , if . We also proved that the Erdos Density Theorem holds in if and only if is strongly reducible.

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Additional Information

**Zhe Dong**

Affiliation:
Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China

Address at time of publication:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Email:
dzhe8@mail.china.com

**Shijie Lu**

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

DOI:
https://doi.org/10.1090/S0002-9939-02-06748-5

Keywords:
Closed maximal triangular algebra,
finite rank operator,
\,
$w^{*}$-closure

Received by editor(s):
December 12, 2000

Received by editor(s) in revised form:
December 16, 2001

Published electronically:
October 1, 2002

Communicated by:
David R. Larson

Article copyright:
© Copyright 2002
American Mathematical Society