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Bounded point evaluations for cyclic operators and local spectra
Author(s):
A.
Bourhim;
C.
E.
Chidume;
E.
H.
Zerouali
Journal:
Proc. Amer. Math. Soc.
130
(2002),
543-548.
MSC (2000):
Primary 47A10;
Secondary 47B20.
Posted:
July 25, 2001
MathSciNet review:
1862135
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Abstract:
In this paper we study the concept of bounded point evaluations for cyclic operators. We give a negative answer to a question of L.R. Williams, Dynamic Systems and Applications 3 (1994), 103-112. Furthermore, we generalize some results of Williams and give a simple proof that nonnormal hyponormal weighted shifts have fat local spectra.
References:
-
- 1.
- I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968. MR 52:15085
- 2.
- J.B. Conway, The Theory of Subnormal Operators, volume 36 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, R.I., 1991. MR 92h:47026
- 3.
- I. Erdelyi and R. Lange, Spectral Decomposition on Banach Spaces, Lecture Notes in Mathematics, vol. 623, Springer-Verlag, New York, (1977). MR 58:2432
- 4.
- M. Radjabalipour, Ranges of Hyponormal Operators, Illinois J. Math. 21(1977), 70-75. MR 56:6449
- 5.
- M. Raphael, Quasisimilarity and Essential Spectra for Subnormal Operators, Indiana Univ. Math. J. 31(1982), 243-246. MR 83d:47031
- 6.
- W. C. Ridge, Approximate Point Spectrum of a Weighted Shift, Trans. Amer. Math. Soc. 147(1970), 349-356. MR 40:7843
- 7.
- A. L. Shields, Weighted Shift Operators and Analytic Function Theory, in Topics in Operator Theory, Mathematical Surveys, no. 13 (ed. C. Pearcy), pp. 49-128. American Mathematical Society, Providence, Rhode Island, 1974. MR 50:14341
- 8.
- J. G. Stampfli, A Local Spectral Theory for Operators. V: Spectral Subspaces for Hyponormal Operators, Trans. Amer. Math. Soc. 21(1976), 285-296. MR 54:8339
- 9.
- T. T. Trent,
 Spaces and Bounded Point Evaluations, Pac. J. Math. 80(1979), 279-292. MR 81j:30054 - 10.
- L. R. Williams, Bounded Point Evaluations and Local Spectra of Cyclic Hyponormal Operators, Dynamic Systems and Applications 3(1994), 103-112. MR 95i:47008
- 11.
- L.R. Williams, The Local Spectra of Pure Quasinormal Operators, J. Math Anal. Appl. 187(1994), 842-850. MR 95h:47029
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Additional Information:
A.
Bourhim
Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
Address at time of publication:
Département de Mathématiques, Université Mohamed V, B.P. 1014, Rabat, Morocco
Email:
bourhim@ictp.trieste.it, abourhim@fsr.ac.ma
C.
E.
Chidume
Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
Email:
chidume@ictp.trieste.it
E.
H.
Zerouali
Affiliation:
Département de Mathématiques, Université Mohamed V, B.P. 1014, Rabat, Morocco
Email:
zerouali@fsr.ac.ma
DOI:
10.1090/S0002-9939-01-06102-0
PII:
S 0002-9939(01)06102-0
Received by editor(s):
July 10, 2000
Posted:
July 25, 2001
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2001,
American Mathematical Society
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