Desch-Schappacher Perturbation of One-Parameter Semigroups on Locally Convex Spaces

Abstract

We prove a Desch-Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one-parameter semigroups which are defined on a sequentially complete locally convex space.

10 pages, revised argument in section 2, results unchanged (proof of Theorem 1, the closedness of operator C)

References in corpus (1)

• Universal extrapolation spaces for C${}_0$-semigroups

Cited by in corpus (6)

• Intermediate and extrapolated spaces for bi-continuous semigroups
• On equicontinuity and tightness of bi-continuous semigroups
• A Desch-Schappacher perturbation theorem for bi-continuous semigroups
• Mixed topologies on Saks spaces of vector-valued functions
• Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions
• The abstract Cauchy problem in locally convex spaces