Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
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 Schmoeger.
References:
[1] G.R. Allan: Holomorphic vector-valued functions on a domain of holomorphy. J. London Math. Soc. 42 (1967), 509–513. DOI 10.1112/jlms/s1-42.1.509 | MR 0215097 | Zbl 0144.37702
[2] J. Diestel, J.J. Uhl, Jr.: Vector measures. Math. Surveys 15, Amer. Math. Soc., Providence, Rhode Island, 1977. MR 0453964
[3] R. Harte: Spectral mapping theorems. Proc. Roy. Irish. Acad. Sect. A 73 (1973), 89–107. MR 0326394 | Zbl 0255.47054
[4] T. Kato: Perturbation theory for nullity, deficiency and other quantities of linear operators. J. Anal. Math. 6 (1958), 261–322. DOI 10.1007/BF02790238 | MR 0107819 | Zbl 0090.09003
[5] V. Kordula, V. Müller: The distance from the Apostol spectrum. Proc. Amer. Math. Soc. (to appear). MR 1322931
[6] M. Mbekhta: Résolvant généralisé et théorie spectrale. J. Operator Theory 21 (1989), 69–105. MR 1002122 | Zbl 0694.47002
[7] V. Müller: On the regular spectrum. J. Operator Theory (to appear). MR 1331783
[8] V. Rakočevič: Generalized spectrum and commuting compact perturbations. Proc. Edinb. Math. Soc. 36 (1993), 197–208. DOI 10.1017/S0013091500018332 | MR 1221044
[9] P. Saphar: Contributions à l’étude des applications linéaires dans un espace de Banach. Bull. Soc. Math. France 92 (1964), 363–384. DOI 10.24033/bsmf.1612 | MR 0187095
[10] Ch. Schmoeger: The stability radius of an operator of Saphar typex. Studia Math. 113 (1995), 169–175. DOI 10.4064/sm-113-2-169-175 | MR 1318422
[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. MR 0993774 | Zbl 0721.46004
Search
Partner of
