Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
169-178
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-05-06
poprawiono
1998-10-23
Twórcy
autor
- Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany, Volker.Goersmeyer@math.uni-karlsruhe.de
autor
- Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany, Lutz.Weis@math.uni-karlsruhe.de
Bibliografia
- [1] H. Alt, Lineare Funktionalanalysis, Springer, Berlin, 1992.
- [2] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
- [3] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
- [4] A. Driouich and O. El-Mennaoui, On the inverse formula of Laplace transforms, preprint.
- [5] O. El-Mennaoui and K. J. Engel, On the characterization of eventually norm continuous semigroups in Hilbert space. Arc. Math. (Basel) 63 (1994), 437-440.
- [6] O. El-Mennaoui and K. J. Engel, Towards a characterization of eventually norm continuous semigroups on Banach spaces, Quaestiones Math. 19 (1996), 183-190.
- [7] J. Martinez and J. Mazon, $C_0$-semigroups norm continuous at infinity, Semigroup Forum 52 (1996), 213-224.
- [8] J. van Neerven, The Asymptotic Behaviour of Semigroups of Linear Operators, Birkhäuser, Basel, 1996.
- [9] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
- [10] L. Weis, A short proof for the stability theorem for positive semigroups on $L_p(ν)$, Proc. Amer. Math. Soc. (1998), to appear.
- [11] L. Weis, Integral operators and changes of density, Indiana Univ. Math. J. 31 (1982), 83-96.
- [12] P. You, Characteristic conditions for $c_0$-semigroups with continuity in the uniform operator topology for t>0, Proc. Amer. Math. Soc. 116 (1992), 991-997.
Typ dokumentu
Bibliografia
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