Invariance of closed convex sets and domination criteria for semigroups |
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| Authors: | El-Maati Ouhabaz |
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| Institution: | (1) SFB 288, Technische Universität Berlin, 136, Straße des 17 Juni, 10623 Berlin, Germany;(2) Max-Planck Arbeitsgruppe, FB Mathematik, Universität Potsdam, 14415 Potsdam, Germany;(3) Present address: Equipe d'Analyse et de Mathématique Appliqués, Université de Marne-la-Valleé, 2, rue de la Butte Verte, 93166 Noisy-le-Grand, France |
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| Abstract: | Let a and b be two positive continuous and closed sesquilinear forms on the Hilbert space H=L
2( ,  ). Denote by T=T(t)
t 0and S=S(t)
t0the semigroups generated by a and b on H. We give criteria in terms of a and b guaranteeing that the semigroup T is dominated by S, i.e. |T(t)f| S(t)|f| for all t0 and f H. The method proposed uses ideas on invariance of closed convex sets of H under semigroups. Applications to elliptic operators and concrete examples are given. |
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| Keywords: | 47A63 47B65 47A15 |
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