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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
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Additional information
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:
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- 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.
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- 6.
- W. C. Ridge, Approximate Point Spectrum of a Weighted Shift, Trans. Amer. Math. Soc. 147(1970), 349-356. MR 40:7843
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- 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.
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- 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
Forward Citation(s): Information for authors on submitting citations The following works have cited this article A. Bourhim, Bounded point evaluations for cyclic Hilbert space operators, Appl. Gen. Topol. 4, no 2, (2003), 301--316. (English) MR 2073580
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