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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Point-spectrum-preserving elementary operators on $B(H)$

Author(s): Qin Wang; Jinchuan Hou
Journal: Proc. Amer. Math. Soc. 126 (1998), 2083-2088.
MSC (1991): Primary 47A10, 47B47
MathSciNet review: 1443414
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Abstract | References | Similar articles | Additional information

Abstract: Let $H$ be an infinite dimensional separable Hilbert space over the complex field. Structure characterizations are given for some elementary operators on $B(H)$ which preserve point spectrum.


References:

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Ming Chu Gao, Numerical range preserving linear maps and spectrum preserving elementary operators on $B(H)$, Chinese Ann. Math. Ser. A, 14 (1993), 295-301. MR 94g:47043

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Jin Chuan Hou, Spectrum preserving elementary operators on $B(H)$, preprint.

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A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. MR 87m:47011

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Chi-Kwong Li and Nam-Kiu Tsing, Linear preserver problems: A brief introduction and some techniques, Linear Alg. Appl., 162-164 (1992), 217-235. MR 93b:15003

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P. \v{S}emrl, Two characterizations of automorphisms on $B(X)$, Studia Mathematica, 105(2) (1993), 143-149. MR 94h:47064

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Additional Information:

Qin Wang
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China
Email: 970005@fudan.edu.cn

Jinchuan Hou
Affiliation: Department of Mathematics, Shanxi Teachers University, Linfen, Shanxi, 041004, People's Republic of China

DOI: 10.1090/S0002-9939-98-04313-5
PII: S 0002-9939(98)04313-5
Keywords: Hilbert space, elementary operator, point spectrum
Received by editor(s): July 14, 1995
Received by editor(s) in revised form: March 15, 1996 and January 2, 1997
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society




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