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On the topological boundary of the one-sided spectrum. (English) Zbl 1008.47003
Summary: It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Ch. Schmoeger.
47A10 Spectrum, resolvent
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[1] G.R. Allan: Holomorphic vector-valued functions on a domain of holomorphy. J. London Math. Soc. 42 (1967), 509-513. · Zbl 0144.37702
[2] J. Diestel, J.J. Uhl, Jr.: Vector measures. Math. Surveys 15, Amer. Math. Soc., Providence, Rhode Island, 1977. · Zbl 0369.46039
[3] R. Harte: Spectral mapping theorems. Proc. Roy. Irish. Acad. Sect. A 73 (1973), 89-107. · Zbl 0255.47054
[4] T. Kato: Perturbation theory for nullity, deficiency and other quantities of linear operators. J. Anal. Math. 6 (1958), 261-322. · Zbl 0090.09003
[5] V. Kordula, V. Müller: The distance from the Apostol spectrum. Proc. Amer. Math. Soc. · Zbl 0861.47008
[6] M. Mbekhta: Résolvant généralisé et théorie spectrale. J. Operator Theory 21 (1989), 69-105. · Zbl 0694.47002
[7] V. Müller: On the regular spectrum. J. Operator Theory · Zbl 0845.47005
[8] V. Rakočevič: Generalized spectrum and commuting compact perturbations. Proc. Edinb. Math. Soc. 36 (1993), 197-208. · Zbl 0794.47003
[9] P. Saphar: Contributions à l’étude des applications linéaires dans un espace de Banach. Bull. Soc. Math. France 92 (1964), 363-384. · Zbl 0139.08502
[10] Ch. Schmoeger: The stability radius of an operator of Saphar typex. Studia Math. 113 (1995), 169-175. · Zbl 0819.47002
[11] N. Tomczak-Jaegermann: Banach-Mazur distances and finite-dimensional operator ideals. Pitman Monographs and Surveys in Pure and Applied Mathematics 38, Longman Scientific & Technical, Harlow, 1989. · Zbl 0721.46004
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