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Periodica Mathematica Hungarica

, Volume 14, Issue 1, pp 101–105 | Cite as

Über Die Konvergenz Operatorwertiger Cosinusfunktionen mit Gestörtem Infinitesimalen Erzeuger

Article

Abstract

On convergence of operator cosine functions with perturbed infinitesimal generator. The question under what kind of perturbations a closed linear operatorA remains of the class of infinitesimal generators of operator cosine functions seems to be a rather difficult one and is unsolved in general. In this note we give bounds for the perturbation of operator cosine functions caused byA-bounded perturbationsT ofA under the assumption thatT + A is also a generator.

AMS (MOS) subject classifications (1980)

Primary 34G10, 39B70 Secondary 47D05 

Key words and phrases

Operator-valued cosine functions second order differential equations in abstract spaces 

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Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • D. Lutz
    • 1
  1. 1.Fachbereich 6 (Mathematik)Universität EssenEssenFederal Republic of Germany

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