Semigroups of sums of two operators with small commutators

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6 Scopus citations


Let A be the generator of a C-semigroup (eAt)t≥0 on a Banach space X and B be a bounded operator in X. Assuming that ∫0∞‖eAt‖‖eBt‖dt<∞ and the commutator AB- BA is bounded and has a sufficiently small norm, we show that ∫0∞‖e(A+B)t‖dt<∞, where (e(A+B)t)t≥0 is the semigroup generated by A+ B. In addition, estimates for the supremum- and L 1 -norms of the difference e ( A + B ) t - e At e Bt are derived.

Original languageEnglish
Pages (from-to)22-30
Number of pages9
JournalSemigroup Forum
Issue number1
StatePublished - 15 Feb 2019


  • Banach space
  • Commutator
  • Perturbations
  • Semigroups

ASJC Scopus subject areas

  • Algebra and Number Theory


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