Spectrum of bilateral shifts with operator-valued weights

Bourhim, A.

doi:10.1090/S0002-9939-06-08230-X

Spectrum of bilateral shifts with operator-valued weights
HTML articles powered by AMS MathViewer

by A. Bourhim PDF

Proc. Amer. Math. Soc. 134 (2006), 2131-2137 Request permission

Abstract:

We describe the spectrum of bilateral operator-weighted shifts.

References

Pietro Aiena, Fredholm and local spectral theory, with applications to multipliers, Kluwer Academic Publishers, Dordrecht, 2004. MR 2070395
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 and C. E. Chidume, The single-valued extension property for bilateral operator weighted shifts, Proc. Amer. Math. Soc. 133 (2005), no. 2, 485–491. MR 2093072, DOI 10.1090/S0002-9939-04-07535-5
A. Bourhim, Local spectra of bilateral operator weighted shifts, Rend. Circ. Mat. Palermo (2) Suppl. 73 (2004), 195–206. MR 2078176
Domingo A. Herrero, Spectral pictures of hyponormal bilateral operator weighted shifts, Proc. Amer. Math. Soc. 109 (1990), no. 3, 753–763. MR 1014644, DOI 10.1090/S0002-9939-1990-1014644-3
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
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
M. Radjabalipour, Ranges of hyponormal operators, Illinois J. Math. 21 (1977), no. 1, 70–75. MR 448140, DOI 10.1215/ijm/1256049502
William C. Ridge, Approximate point spectrum of a weighted shift, Trans. Amer. Math. Soc. 147 (1970), 349–356. MR 254635, DOI 10.1090/S0002-9947-1970-0254635-5
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