Bishop's property () and essential spectra

of quasisimilar operators

Authors:
Lin Chen and Yan Zikun

Journal:
Proc. Amer. Math. Soc. **128** (2000), 485-493

MSC (1991):
Primary 47B40, 47A10

DOI:
https://doi.org/10.1090/S0002-9939-99-05047-9

Published electronically:
May 19, 1999

MathSciNet review:
1625717

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We analyze the notion of Bishop's property () to obtain some new concepts. We describe some conditions in terms of these concepts for an operator to have its essential spectrum (spectrum) contained in the essential spectrum (spectrum) of every operator quasisimilar to it. A subfamily of such operators is proved to be dense in .

**1.**B. Sz-Nagy and C. Foias,*Harmonic Analysis of Operators on Hilbert Space*, North Holland-American Elsevier, New York, 1970 (English edition). MR**43:947****2.**Liming Yang,*Quasisimilarity of hyponormal and subdecomposable operators*, J. Functional Analysis**112**(1993), 204-217. MR**94c:47033****3.**M. Putinar,*Quasisimilarity of tuples with Bishop's property*, Integral Equations and Operator Theory**15**(1992), 1047-1052. MR**94a:47036****4.**E. Bishop,*A duality theorem for an arbitrary operator*, Pacific J. Math.**9**(1959), 379-397. MR**22:8339****5.**J. Eschmeier,*A decomposable Hilbert space operator which is not strongly decomposable*, Integral Equations and Operator Theory**11**(1988), 161-172. MR**89b:47051****6.**C. Apostol,*The correction by compact perturbation of the singular behavior of operators*, Rev. Roum. Math. Pures et Appl.**21**(1976), 155-175. MR**58:7180****7.**Shan Li Sun,*The single-valued extension property and spectral manifolds*, Proc. Amer. Math. Soc.**118**(1993), 77-87. MR**93f:47004****8.**N. Dunford and J. T. Schwarz,*Linear Operators, Part III*, Wiley-InterScience, New York, 1971. MR**90g:47001c****9.**T. Kato,*Perturbation Theory of Linear Operators*, Springer-Verlag, Berlin, New York, 1995 (reprint of 1980 edition). MR**96a:47025****10.**L.A. Fialkow,*A note on quasisimilarity of operators*, Acta Sci. Math.**39**(1977), 67-85. MR**56:3661****11.**D.A. Herrero,*On the essential spectra of quasisimilar operators*, Can. J. Math.**40**(1988), 1436-1457. MR**90b:47006****12.**D.A. Herrero,*Quasisimilar operators with different spectra*, Acta Sci. Math.**41**(1979), 101-118. MR**80e:47002****13.**C. Apostol and B. Morrel,*On uniform approximation of operators by simple models*, Indiana Univ. Math. J.**26**(1977), 427-442. MR**55:8853**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
47B40,
47A10

Retrieve articles in all journals with MSC (1991): 47B40, 47A10

Additional Information

**Lin Chen**

Affiliation:
Department of Mathematics, Fujian Normal University, Fuzhou, 350007, The People’s Republic of China

Email:
xhyan@fjtu.edu.cn

**Yan Zikun**

Affiliation:
Department of Mathematics, Fujian Normal University, Fuzhou, 350007, The People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9939-99-05047-9

Keywords:
Quasisimilarity,
essential spectra,
subdecomposability

Received by editor(s):
March 27, 1998

Published electronically:
May 19, 1999

Additional Notes:
This research was supported by the National Natural Science Foundation of China

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society