## Abstract

We prove that a strongly continuous semigroup of linear operators on a Hilbert space is weakly L^{p}-stable for some p ε{lunate} [1, ∞) if and only if the semigroup is exponentially stable. As an application, we prove that the Cauchy problems associated with the semigroup are well posed on the infinite time interval (- ∞, 0] if and only if the semigroup is exponentially stable.

Original language | English |
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Pages (from-to) | 269-285 |

Number of pages | 17 |

Journal | Journal of Differential Equations |

Volume | 76 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1988 |

Externally published | Yes |

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