Norm continuity of $c_0$-semigroups

V. Goersmeyer; L. Weis

ArticleOriginal scientific text

Title

Norm continuity of $c_{0}$ -semigroups

Authors ¹, ¹

Affiliations

Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany

Abstract

We show that a positive semigroup

T_{t}

on

L_{p} (Ω, ν)

with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of "smoothing properties" of certain convolution operators on general Banach spaces and an extrapolation result for the

L_{p}

-scale, which may be of independent interest.

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Title

Norm continuity of c0-semigroups

Affiliations

Abstract

Bibliography

Norm continuity of $c_{0}$ -semigroups