Characterization of Gaussian semigroups on separable Banach spaces

Abstract

Let E be a separable real Banach space and denote by BUC (E) the space of bounded and uniformly continuous functions on E. For a C 0-semigroup \((T(t))_{t\ge 0}\) acting on BUC(E), we obtain necessary and sufficient conditions ensuring that \((T(t))_{t \ge 0}\) is Gaussian.

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Correspondence to Mohamed Abouabassi or Omar El-Mennaoui or Valentin Keyantuo.

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Abouabassi, M., El-Mennaoui, O. & Keyantuo, V. Characterization of Gaussian semigroups on separable Banach spaces. J.evol.equ. 4, 157–167 (2004). https://doi.org/10.1007/s00028-003-0123-x

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Mathematics Subject Classification (2000):

  • Primary 47D03
  • 47D06
  • 60B11