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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-03-07275-7

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