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Completely rank nonincreasing linear maps on nest algebras
Author(s):
Jinchuan
Hou;
Jianlian
Cui
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1419-1428.
MSC (2000):
Primary 47B48, 47L35
Posted:
November 4, 2003
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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.
References:
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- 3.
- Davidson, K. R., Nest Algebras, Pitman Research Notes in Mathematics, Vol. 191, Longman Scientific and Technical, London/New York, 1988. MR 90f:47062
- 4.
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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:
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
Posted:
November 4, 2003
Additional Notes:
This work is supported by NNSFC and PNSFS
Communicated by:
David R. Larson
Copyright of article:
Copyright
2003,
American Mathematical Society
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