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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: June 17, 2004
MathSciNet review: 2073302
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Abstract: It is proved that a nest $\mathcal N$ on a separable complex Hilbert space $\mathcal H$ has the left (resp. right) partial factorization property, which means that for every invertible operator $ T$ from $\mathcal H$ onto a Hilbert space $\mathcal K$ there exists an isometry (resp. a coisometry) $U$ from $\mathcal H $ into $\mathcal K$ such that both $U^*T$ and $T^{-1}U$ are in the associated nest algebra $Alg \mathcal N$ 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: http://dx.doi.org/10.1090/S0002-9939-04-07446-5
PII: S 0002-9939(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