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Essentially Normal Operator + Compact Operator = Strongly Irreducible Operator
Author(s):
Chunlan
Jiang;
Shunhua
Sun;
Zongyao
Wang
Journal:
Trans. Amer. Math. Soc.
349
(1997),
217-233.
MSC (1991):
Primary 47A10, 47A55, 47A58
MathSciNet review:
1376549
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Abstract:
It is shown that given an essentially normal operator  with connected spectrum, there exists a compact operator  such that  is strongly irreducible.
References:
- 1.
- R. A. Adams, Sobolev spaces, Academic Press, New York-San Francisco-London, 1975. MR 56:9247
- 2.
- C. Apostol, L. A. Fialkow, D. A. Herrero and D. Voiculescu, Approximation of Hilbert space operators, II, Research Notes in Math., vol. 102, Pitman Books, Ltd., London-Boston-Melbourne, 1984. MR 85m:47002
- 3.
- L. G. Brown, R. G. Douglas, and P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of
 -algebras, Proceedings of a Conference on Operator Theory, Halifax, Nova Scotia, 1973, Lect. Notes in Math., vol. 345, Springer-Verlag, 1973, pp. 58-128. MR 52:1378 - 4.
- J. B. Conway, Subnormal operators, Research Notes in Math. 51 (1981). MR 83i:47030
- 5.
- M. Cowen and R. G. Douglas, Complex geometry and operator theory, Bull. Amer. Math. Soc. 83 (1977), 131-133. MR 58:17885
- 6.
- M. Cowen and R. G. Douglas, Complex geometry and operator theory, Acta Math. 141 (1978), 187-261. MR 80f:47012
- 7.
- R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York and London, 1972. MR 50:14335
- 8.
- C. K. Fong and C. L. Jiang, Approximation by Jordan type operators, Houston J. Math. 19 (1993), 51-62. MR 94d:47011
- 9.
- C. K. Fong and C. L. Jiang, On irreducible operators, Northeastern Math. J. 8 (5) (1992), 385-390. MR 94b:47023
- 10.
- F. Gilfeather, Strong reducibility of operators, Indiana Univ. Math. J. 22 (1972), 393-397. MR 46:2460
- 11.
- P. R. Halmos, Irreducible operators, Mich. Math. J. 15 (1968). MR 37:6788
- 12.
- D. A. Herrero, Approximation of Hilbert space operators, Vol. 1, 2nd ed., Pitman Res. Notes Math. 224, Longman Sci. Tech., Harlow, Essex, 1989. MR 91k:47002
- 13.
- D. A. Herrero and C. L. Jiang, Limits of strongly irreducible operators and the Riesz decomposition theorem, Mich. Math. J. 37 (1990), 283-291. MR 91k:47035
- 14.
- D. A. Herrero, T. J. Taylor and Z. Y. Wang, Variation of the point spectrum under compact perturbations, Topics in operator theory, Constantin Apostol Memorial Issue, OT: Advances and Applications, vol. 32, Birkhäuser-Verlag, Basel-Boston-Stuttgart, 1988, pp. 113-158. MR 89h:47018
- 15.
- Z. J. Jiang, A lecture on operator theory, The report in the seminar of functional analysis in Jilin Univ., Chang Chun, 1979.
- 16.
- Z. J. Jiang and S. L. Sun, On completely irreducible operators, Acta Scientiarum Naturalium Universitatis Jilinensis 4 (1992), 20-29.
- 17.
- C. L. Jiang, Strongly irreducible operators and Cowen-Douglas operators, Northeastern Math. J. 7 (1) (1991), 1-3. MR 92e:47024
- 18.
- C. L. Jiang, Similarity, reducibility and approximation of Cowen-Douglas operators, J. Operator Theory 32 (1994), 77-89. MR 96d:47013
- 19.
- C. L. Jiang and Z. Y. Wang, The spectral pictures of completely irreducible operators and decomposition theorem of Hilbert space operators, Northeastern Math. J. 10 (2) (1994), 145-148.
- 20.
- C. L. Jiang and Z. Y. Wang, A class of strongly irreducible operators with nice property, J. Operator Theory (to appear).
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Additional Information:
Chunlan
Jiang
Affiliation:
Department of Mathematics, Jilin University, Changchun 130023, P.R. of China
Shunhua
Sun
Affiliation:
Department of Mathematics, Sichuan University, Chengdu 610064, P.R. of China
Zongyao
Wang
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, P.R. of China
DOI:
10.1090/S0002-9947-97-01754-6
PII:
S 0002-9947(97)01754-6
Keywords:
Essentially normal operator,
strongly irreducible operator,
Sobolev space,
Cowen-Douglas operator,
subnormal operator,
Rosenblum operator
Received by editor(s):
May 25, 1995
Additional Notes:
The research supported by National Natural Science Foundation of China.
Copyright of article:
Copyright
1997,
American Mathematical Society
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