Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-27T18:59:01.249Z Has data issue: false hasContentIssue false
  • English
  • Français

Monotone continuity of the spectral resolution and the eigenvalues

Published online by Cambridge University Press:  14 November 2011

Joachim Weidmann
Joachim Weidmann
Affiliation:
Fachbereich Mathematik der Universität, Robert-Mayer-Straße 6–10, D6000 Frankfurt am Main, B.R.D.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Let (Tn) be a non-decreasing sequence of self-adjoint operators which are semi-bounded from below and converge to some self-adjoint operator T in the sense of strong resolvent convergence. For every λ which is eventually below the essential spectrum of Tn it is shown that ‖En(λ)−E(λ)‖→0 for n→∞, where En(·) and E(·) are the spectral resolution of Tn and T, respectively.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 1-2 , 1980 , pp. 131 - 136
Copyright
Copyright © Royal Society of Edinburgh 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Fans, W. G.. Self-adjoint operators. Lecture Notes in Mathematics 433 (Berlin: Springer, 1976).Google Scholar
2Kato, T.. Perturbation Theory for Linear Operators, 2nd edn (Berlin: Springer, 1976).Google Scholar
3Weidmann, J.. Lineare Operatoren in Hilberträumen (Stuttgart: Teubner, 1976).Google Scholar