Remarks on resolvent positive operators and their perturbation

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21 Scopus citations

Abstract

We consider positive perturbations A = B + C of resolvent positive operators B by positive operators C : D(A) → X and in particular study their spectral properties. We characterize the spectral bound of A, s(A), in terms of the resolvent outputs F(λ) = C(λ - B)-1 and derive conditions for s(A) to be an eigenvalue of A and a (first order) pole of the resolvent of A. On our way we show that the spectral radii of a completely monotonie operator family form a superconvex function. Our results will be used in forthcoming publications to study the spectral and large-time properties of positive operator semigroups.

Original languageEnglish (US)
Pages (from-to)73-90
Number of pages18
JournalDiscrete and Continuous Dynamical Systems
Volume4
Issue number1
StatePublished - Dec 1 1998

Keywords

  • Asynchronous exponential growth
  • Balanced exponential growth
  • Growth bounds
  • Integrated semigroups
  • Positive perturbation
  • Resolvent outputs
  • Resolvent positive operators
  • Semigroups
  • Spectral bound

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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