Mean stability of semigroups

Shmuel Kantorovitz, Serguei Piskarev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let T(·) be a bounded C0-semigroup on the Banach space X, with generator A. It is shown that the denseness of range A is necessary and sufficient for the semigroup's mean stability with respect to suitable weights. Analogous results are valid for power bounded operators, tensor product semigroups, and cosine operator functions.

Original languageEnglish
Pages (from-to)89-103
Number of pages15
JournalTaiwanese Journal of Mathematics
Issue number1
StatePublished - Mar 2002


  • C-semigroup
  • Cosine operator function
  • Generator
  • Mean stability
  • Point spectrum
  • Power bounded operator
  • Residual spectrum
  • Semigroup
  • Tensor product of semigroups


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