Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-11T02:58:07.606Z Has data issue: false hasContentIssue false
  • English
  • Français

On Operators with Spectral Square but without Resolvent Points

Published online by Cambridge University Press:  20 November 2018

Paul Binding  and
Vladimir Strauss
Paul Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB e-mail: binding@ucalgary.ca
Vladimir Strauss
Affiliation:
Department of Pure and Applied Mathematics, Simón Bolívar University, Caracas, Venezuela e-mail: str@usb.ve
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.

Decompositions of spectral type are obtained for closed Hilbert space operators with empty resolvent set, but whose square has closure which is spectral. Krein space situations are also discussed.

Keywords

47A0547A1547B4047B5046C20unbounded operatorsclosed operatorsspectral resolutionindefinite metric
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 1 , 01 February 2005 , pp. 61 - 81
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Akhiezer, N. I. and Glazman, I. M., Theory of linear operators in Hilbert space. vol. 2, Pitman, Boston, 1981.Google Scholar
[2] Atkinson, F. V. and Mingarelli, A. B., Asymptotics of the number of zeros and of the eigenvalues of general weighted Sturm-Liouville problems. J. Reine Angew.Math. 375/376 (1987), 380–393.Google Scholar
[3] Azizov, T. Ya. and Iokhvidov, I. S., Linear operators in spaces with an indefinite metric. JohnWiley and Sons, Chichester, 1989.Google Scholar
[4] Bognár, J., Indefinite inner product spaces. ergeb. math. Grenzgeb., 78, Springer-Verlag, New York, 1974.Google Scholar
[5] Bognár, J., A proof of the spectral theorem for J-positive operators. Acta Sci. Math. (Szeged) 45 (1983), 75–80.Google Scholar
[6] Ćurgus, B. and Langer, H., A Kreĭn space approach to symmetric ordinary differential operators with an indefinite weight function. J. Differential Equations 79 (1989), 31–61.Google Scholar
[7] Dunford, N. and Schwartz, J. T., Linear Operators. I. General Theory, Interscience, London, 1958.Google Scholar
[8] Freiling, G. and Yurko, V., On constructing differential equations with singularities from incomplete spectral information. Inverse Problems 14 (1998), 1131–1150.Google Scholar
[9] Langer, H., Spectral functions of definitizable operators in Krein space. Lect. Notes in Math. 948, Springer, Berlin, 1982, pp. 1–46.Google Scholar
[10] Karapetiants, N. and Samko, S., Equations with involutive operators. Birkhäuser, Boston, 2001.Google Scholar
[11] Kato, T., Perturbation theory for linear operators. Springer-Verlag, New York, 1966.Google Scholar
[12] Kreyszig, E., Introductory functional analysis with applications. JohnWiley and Sons, New York, 1978.Google Scholar
[13] Kuzhel, A. V. and Kuzhel, S. A., Regular extensions of Hermitian operators. VSP, Utrecht, 1998.Google Scholar
[14] Naimark, M. A., Normed algebras. Wolters-Nordhoff, 1972.Google Scholar