×

zbMATH — the first resource for mathematics

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.
MSC:
47A10 Spectrum, resolvent
PDF BibTeX Cite
Full Text: DOI EuDML
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.