Weyl’s theorem for perturbations of paranormal operators
HTML articles powered by AMS MathViewer
- by Pietro Aiena and Jesús R. Guillen
- Proc. Amer. Math. Soc. 135 (2007), 2443-2451
- DOI: https://doi.org/10.1090/S0002-9939-07-08582-6
- Published electronically: April 10, 2007
- PDF | Request permission
Abstract:
A bounded linear operator $T\in L(X)$ on a Banach space $X$ is said to satisfy “Weyl’s theorem” if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if $T$ is a paranormal operator on a Hilbert space, then $T+K$ satisfies Weyl’s theorem for every algebraic operator $K$ which commutes with $T$.References
- Pietro Aiena, Fredholm and local spectral theory, with applications to multipliers, Kluwer Academic Publishers, Dordrecht, 2004. MR 2070395
- Pietro Aiena, Classes of operators satisfying $a$-Weyl’s theorem, Studia Math. 169 (2005), no. 2, 105–122. MR 2140450, DOI 10.4064/sm169-2-1
- Pietro Aiena, Maria Luisa Colasante, and Manuel González, Operators which have a closed quasi-nilpotent part, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2701–2710. MR 1900878, DOI 10.1090/S0002-9939-02-06386-4
- T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169–178. MR 320800
- S. L. Campbell and B. C. Gupta, On $k$-quasihyponormal operators, Math. Japon. 23 (1978/79), no. 2, 185–189. MR 517798
- N. N. Chourasia and P. B. Ramanujan, Paranormal operators on Banach spaces, Bull. Austral. Math. Soc. 21 (1980), no. 2, 161–168. MR 574835, DOI 10.1017/S0004972700005980
- L. A. Coburn, Weyl’s theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288. MR 201969
- Raúl E. Curto and Young Min Han, Weyl’s theorem for algebraically paranormal operators, Integral Equations Operator Theory 47 (2003), no. 3, 307–314. MR 2012841, DOI 10.1007/s00020-002-1164-1
- B. P. Duggal, Roots of contractions with Hilbert-Schmidt defect operator and $C_{\bfcdot 0}$ completely non-unitary part, Comment. Math. (Prace Mat.) 36 (1996), 85–106. MR 1427824
- Nelson Dunford, Spectral theory. II. Resolutions of the identity, Pacific J. Math. 2 (1952), 559–614. MR 51435
- Nelson Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321–354. MR 63563
- James K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), no. 1, 61–69. MR 374985
- Takayuki Furuta, Masatoshi Ito, and Takeaki Yamazaki, A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1 (1998), no. 3, 389–403. MR 1688255
- Harro G. Heuser, Functional analysis, A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1982. Translated from the German by John Horváth. MR 640429
- Kjeld B. Laursen and Michael M. Neumann, An introduction to local spectral theory, London Mathematical Society Monographs. New Series, vol. 20, The Clarendon Press, Oxford University Press, New York, 2000. MR 1747914
- Kirti K. Oberai, On the Weyl spectrum. II, Illinois J. Math. 21 (1977), no. 1, 84–90. MR 428073
- Kirti K. Oberai, Spectral mapping theorem for essential spectra, Rev. Roumaine Math. Pures Appl. 25 (1980), no. 3, 365–373. MR 577924
- Mourad Oudghiri, Weyl’s and Browder’s theorems for operators satisfying the SVEP, Studia Math. 163 (2004), no. 1, 85–101. MR 2047466, DOI 10.4064/sm163-1-5
- Mourad Oudghiri, Weyl’s theorem and perturbations, Integral Equations Operator Theory 53 (2005), no. 4, 535–545. MR 2187437, DOI 10.1007/s00020-004-1342-4
Bibliographic Information
- Pietro Aiena
- Affiliation: Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
- Email: paiena@unipa.it
- Jesús R. Guillen
- Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad UCLA, Merida, Venezuela
- Email: rguillen@ula.ve
- Received by editor(s): June 7, 2005
- Received by editor(s) in revised form: November 21, 2005
- Published electronically: April 10, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2443-2451
- MSC (2000): Primary 47A10, 47A11; Secondary 47A53, 47A55
- DOI: https://doi.org/10.1090/S0002-9939-07-08582-6
- MathSciNet review: 2302565