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

 

Completely rank nonincreasing linear maps on nest algebras


Authors: Jinchuan Hou and Jianlian Cui
Journal: Proc. Amer. Math. Soc. 132 (2004), 1419-1428
MSC (2000): Primary 47B48, 47L35
Published electronically: November 4, 2003
MathSciNet review: 2053348
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Abstract: In this paper, the completely rank nonincreasing bounded linear maps on nest algebras acting on separable Hilbert spaces are characterized, and an affirmative answer to a problem posed by Hadwin and Larson is given for the case of such nest algebras.


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Additional Information

Jinchuan Hou
Affiliation: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
Address at time of publication: Department of Mathematics, Shanxi University, Taiyuan 030000, People’s Republic of China
Email: jhou@dns.sxtu.edu.cn

Jianlian Cui
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Address at time of publication: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
Email: cuijl@dns.sxtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07275-7
PII: S 0002-9939(03)07275-7
Keywords: Nest algebras, rank, linear maps
Received by editor(s): October 8, 2001
Received by editor(s) in revised form: January 8, 2003
Published electronically: November 4, 2003
Additional Notes: This work is supported by NNSFC and PNSFS
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society