| Title:
|
On the topological boundary of the one-sided spectrum (English) |
| Author:
|
Müller, Vladimír |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
561-568 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| MSC:
|
47A10 |
| idZBL:
|
Zbl 1008.47003 |
| idMR:
|
MR1708358 |
| . |
| Date available:
|
2009-09-24T10:25:24Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127510 |
| . |
| Reference:
|
[1] G.R. Allan: Holomorphic vector-valued functions on a domain of holomorphy.J. London Math. Soc. 42 (1967), 509–513. Zbl 0144.37702, MR 0215097, 10.1112/jlms/s1-42.1.509 |
| Reference:
|
[2] J. Diestel, J.J. Uhl, Jr.: Vector measures.Math. Surveys 15, Amer. Math. Soc., Providence, Rhode Island, 1977. MR 0453964 |
| Reference:
|
[3] R. Harte: Spectral mapping theorems.Proc. Roy. Irish. Acad. Sect. A 73 (1973), 89–107. Zbl 0255.47054, MR 0326394 |
| Reference:
|
[4] T. Kato: Perturbation theory for nullity, deficiency and other quantities of linear operators.J. Anal. Math. 6 (1958), 261–322. Zbl 0090.09003, MR 0107819, 10.1007/BF02790238 |
| Reference:
|
[5] V. Kordula, V. Müller: The distance from the Apostol spectrum.Proc. Amer. Math. Soc. (to appear). MR 1322931 |
| Reference:
|
[6] M. Mbekhta: Résolvant généralisé et théorie spectrale.J. Operator Theory 21 (1989), 69–105. Zbl 0694.47002, MR 1002122 |
| Reference:
|
[7] V. Müller: On the regular spectrum.J. Operator Theory (to appear). MR 1331783 |
| Reference:
|
[8] V. Rakočevič: Generalized spectrum and commuting compact perturbations.Proc. Edinb. Math. Soc. 36 (1993), 197–208. MR 1221044, 10.1017/S0013091500018332 |
| Reference:
|
[9] P. Saphar: Contributions à l’étude des applications linéaires dans un espace de Banach.Bull. Soc. Math. France 92 (1964), 363–384. MR 0187095, 10.24033/bsmf.1612 |
| Reference:
|
[10] Ch. Schmoeger: The stability radius of an operator of Saphar typex.Studia Math. 113 (1995), 169–175. MR 1318422, 10.4064/sm-113-2-169-175 |
| Reference:
|
[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, MR 0993774 |
| . |
