Nests with the partial factorization property

Authors:
Guoxing Ji and Xiuhong Sun

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3275-3281

MSC (2000):
Primary 47L35

DOI:
https://doi.org/10.1090/S0002-9939-04-07446-5

Published electronically:
June 17, 2004

MathSciNet review:
2073302

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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that a nest on a separable complex Hilbert space has the left (resp. right) partial factorization property, which means that for every invertible operator from onto a Hilbert space there exists an isometry (resp. a coisometry) from into such that both and are in the associated nest algebra if and only if it is atomic (resp. countable).

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Additional Information

**Guoxing Ji**

Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, People’s Republic of China

Email:
gxji@snnu.edu.cn

**Xiuhong Sun**

Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9939-04-07446-5

Keywords:
Nest,
nest algebra,
left (resp. right) partial factorization,
factorization

Received by editor(s):
April 30, 2003

Received by editor(s) in revised form:
July 11, 2003

Published electronically:
June 17, 2004

Additional Notes:
This research was supported in part by the National Natural Science Foundation of China (No. 10071047), the Excellent Young Teachers Program of MOE, P.R.C. and the China Scholarship Council

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society