Bounded point evaluations for cyclic Hilbert space operators


  • A. Bourhim Universite Mohamed



Cyclic operator, Bounded point evaluation, Single-valued extension property, Bishop's property (β)


In this talk, to be given at a conference at Seconda Università degli Studi di Napoli in September 2001, we shall describe the set of analytic bounded point evaluations for an arbitrary cyclic bounded linear operator T on a Hilbert space H and shall answer some questions due to L. R. Williams.


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Author Biography

A. Bourhim, Universite Mohamed

Departement de Mathematiques

The Abdus Salam International Centre for Theoretical Physics, Italy (


P. Aiena and O. Monsalve, Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), 435-448.

A. Bourhim, Bounded point evaluations and local spectral theory, 1999-2000 DICTP Diploma thesis, (available on: http:/

A. Bourhim, C. E. Chidume and E. H. Zerouali, Bounded point evaluations for cyclic operators and local spectra, Proc. Amer. Math. Soc. 130 (2002), 543-548.

A. Bourhim, Points d'évaluations bornées des opérateurs cycliques et comportement radial des fonctions dans la classe de Nevalinna Ph.D. Thesis, Université Mohammed V, Morocco, 2001.

J. Bran, Subnormal operators, Duke Math. J. 22 (1955), 75-94.

S. Clary, Equality of spectra of quasisimilar hyponormal operators, Proc. Amer. Math. Soc., 53 (1975), 88-90.

I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.

J. B. Conway, The Theory of Subnormal Operators, volume 36 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, R.I, 1991.

B. P. Duggal, p-hyponormal operators satisfy Bishop's condition (β), Integral Equations Operator Theory 40 (2001), 436-440.

J. K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61-69.

P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, New York, 1982.

D. E. Herrero, On multicyclic operators, Integral Equations and Operator Theory, 1/1 (1978), 57-102.

K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monograph New Series 20 (2000).

M. Putinar, Hyponormal operators are subscalar, J. Operator Theory, 12 (1984), 385-395.

C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323-330.

M. Raphael, Quasisimilarity and essential spectra for subnormal operators, Indiana Univ. Math. J. 31 (1982), 243-246.

W. C. Ridge, Approximate point spectrum of a weighted shift, Trans. Amer. Math. Soc. 147 (1970), 349-356.

A. L. Shields, Weighted shift operators and analytic function theory, in Topics in Operator Theory, Mathematical Surveys, N0 13 (ed. C. Pearcy), pp. 49-128. American Mathematical Society, Providence, Rhode Island, 1974.

J. G. Stampfli, On Hyponormal and Toeplitz operators, Math. Ann. 183 (1969), 328-336.

T. T. Trent, H2(μ) Spaces and bounded point evaluations, Pac. J. Math., 80 (1979), 279-292.

L. R. Williams, Bounded point evaluations and local spectra of cyclic hyponormal operators, Dynamic Systems and Applications 3 (1994), 103-112.

L. R. Williams, Subdecomposable operators and rationally invariant subspaces, Operator theory: Adv. Appl., 115 (2000), 297-309.

L. Yang, Hyponormal and subdecomposable operators, J. Functional Anal. 112 (1993), 204- 217.




How to Cite

A. Bourhim, “Bounded point evaluations for cyclic Hilbert space operators”, Appl. Gen. Topol., vol. 4, no. 2, pp. 301–316, Oct. 2003.



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