The single-valued extension property for bilateral operator weighted shifts
HTML articles powered by AMS MathViewer
- by A. Bourhim and C. E. Chidume
- Proc. Amer. Math. Soc. 133 (2005), 485-491
- DOI: https://doi.org/10.1090/S0002-9939-04-07535-5
- Published electronically: September 8, 2004
- PDF | Request permission
Abstract:
In this paper, we give necessary and sufficient conditions for a bilateral operator weighted shift to enjoy the single-valued extension property.References
- P. Aiena, T. L. Miller and M. M. Neumann, On a localized single-valued extension property, Proc. Royal Irish Acad. (to appear).
- Pietro Aiena and Ennis Rosas, Single-valued extension property at the points of the approximate point spectrum, J. Math. Anal. Appl. 279 (2003), no. 1, 180–188. MR 1970499, DOI 10.1016/S0022-247X(02)00708-4
- Pietro Aiena and Osmin Monsalve, Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), no. 2, 435–448. MR 1786074, DOI 10.1006/jmaa.2000.6966
- Asher Ben-Artzi and Israel Gohberg, Dichotomy, discrete Bohl exponents, and spectrum of block weighted shifts, Integral Equations Operator Theory 14 (1991), no. 5, 613–677. MR 1118967, DOI 10.1007/BF01200554
- A. Bourhim, On the local spectral properties of weighted shift operators, (submitted).
- Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
- James K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), no. 1, 61–69. MR 374985, DOI 10.2140/pjm.1975.58.61
- Jue Xian Li, The single valued extension property for operator weighted shifts, Northeast. Math. J. 10 (1994), no. 1, 99–103. MR 1294367
- 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
- Jue Xian Li, You Qing Ji, and Shan Li Sun, The essential spectrum and Banach reducibility of operator weighted shifts, Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 3, 413–424. MR 1852955, DOI 10.1007/s101149900033
- Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899
Bibliographic Information
- A. Bourhim
- Affiliation: The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
- MR Author ID: 685154
- Email: bourhim@ictp.trieste.it
- C. E. Chidume
- Affiliation: The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
- MR Author ID: 232629
- Email: chidume@ictp.trieste.it
- Received by editor(s): August 29, 2003
- Received by editor(s) in revised form: October 14, 2003
- Published electronically: September 8, 2004
- Additional Notes: This research was supported in part by the Abdus Salam ICTP, Trieste, Italy
- Communicated by: Joseph A. Ball
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 485-491
- MSC (2000): Primary 47A10; Secondary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-04-07535-5
- MathSciNet review: 2093072