Norm continuity of $c_0$-semigroups

• Autorzy: V. Goersmeyer , L. Weis
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 47B65: Positive operators and order-bounded operators
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 134
• Numer: 2
• Strony: 169-178

Daty

wydano

1999

otrzymano

1998-05-06

poprawiono

1998-10-23

Twórcy

autor

V. Goersmeyer

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

autor

L. Weis

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

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