## Abstract

Suppose that {T_{t} : t ≥ 0} is a symmetric diffusion semigroup on L ^{2}(X) and denote by T̃_{t}:t ≥ 0 its tensor product extension to the Bochner space L^{p}(X,B), where B belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf-Dunford-Schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of T̃_{t}:t ≥ 0 on L ^{p}(X,B). As an application, we show that such continuations exhibit pointwise convergence.

Original language | English |
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Pages (from-to) | 933-949 |

Number of pages | 17 |

Journal | Mathematische Zeitschrift |

Volume | 261 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2009 |

Externally published | Yes |

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