Continuous extension of a densely parameterized semigroup

Eliahu Levy, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over R +.

Original languageEnglish
Pages (from-to)276-284
Number of pages9
JournalSemigroup Forum
Volume78
Issue number2
DOIs
StatePublished - 1 Mar 2009
Externally publishedYes

Keywords

  • Contraction semigroup
  • Densely defined
  • Nonlinear semigroup extension

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