Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-29T04:15:36.629Z Has data issue: false hasContentIssue false
  • English
  • Français

Lomonosov’s Techniques and Burnside’s Theorem

Published online by Cambridge University Press:  20 November 2018

Mikael Lindström  and
Georg Schlüchtermann
Mikael Lindström
Affiliation:
Department of Mathematics Åbo Akademi University FIN-20500 Åbo Finland, email: [email protected]
Georg Schlüchtermann
Affiliation:
Mathematisches Institut der Universität München Theresienstr. 39 D-80333 München Germany, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we give a proof of Lomonosov’s extension of Burnside’s theoremto infinite dimensional Banach spaces.

Keywords

47A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 87 - 89
Copyright
Copyright © Canadian Mathematical Society 2000

References

[B] Brown, S. W., Lomonosov's theorem and essentially normal operators. New Zealand J. Math. 23 (1994), 11–18.Google Scholar
[CLP] Chevreau, B., Li, W. S. and Pearcy, C., A new Lomonosov lemma. J.Operator Theory, (to appear).Google Scholar
[K] Kato, T., Perturbation theory for linear operators. Springer-Verlag, Berlin, Heidelberg, New York, 1966.Google Scholar
[LS] Lebow, A. and Schechter, M., Semigroups of operators and measures of non-compactness. J. Funct. Anal. 7 (1971), 1–26.Google Scholar
[L1] Lomonosov, V., Invariant subspaces for operators commuting with compact operators. Functional Anal. Appl. 7 (1973), 213–214.Google Scholar
[L2] Lomonosov, V., An extension of Burnside's theorem to infinite dimensional spaces. Israel J. Math. 75 (1991), 329–339.Google Scholar
[RR] Radjavi, H. and Rosenthal, P., Invariant Subspaces. Springer-Verlag, New York, 1973.Google Scholar
[R] Rudin, W., Functional Analysis. McGraw-Hill, New York, 1973.Google Scholar
[S] Simonic, A., An extension of Lomonosov's techniques to non-compact operators. Trans. Amer.Math. Soc. 348 (1996), 975–995.Google Scholar
[V] Voigt, J., A perturbation theorem for the essential spectral radius of the strongly continuous semigroups. Monatsh.Math. 90 (1980), 153–161.Google Scholar
[W] Weis, L., A generalization of the Vidav-Jörgens perturbation theorem for semigroups and its application to transport theory. J. Math. Anal. Appl. 129 (1988), 6–23.Google Scholar