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Point-spectrum-preserving elementary operators on
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:
Let be an infinite dimensional separable Hilbert space over the complex field. Structure characterizations are given for some elementary operators on which preserve point spectrum.
References:
- 1.
- B. Aupetit and H. du Tu. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math., 109(1) (1994), 91-100. MR 95c:46070
- 2.
- Ming Chu Gao, Numerical range preserving linear maps and spectrum preserving elementary operators on
, Chinese Ann. Math. Ser. A, 14 (1993), 295-301. MR 94g:47043 - 3.
- Jin Chuan Hou, Rank preserving linear maps on
, Sci. China Ser. A, 32 (1989), 929-940. MR 92b:47052 - 4.
- Jin Chuan Hou, Spectrum preserving elementary operators on
, preprint. - 5.
- A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. MR 87m:47011
- 6.
- 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
- 7.
- P. \v{S}emrl, Two characterizations of automorphisms on
, Studia Mathematica, 105(2) (1993), 143-149. MR 94h:47064 - 8.
- M. Takesaki, Theory of Operator Algebras , Springer-Verlag, New York, 1979. MR 81e:46038
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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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