, Volume 5, Issue 6, pp 611-625

Invariance of closed convex sets and domination criteria for semigroups

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Abstract

Let a and b be two positive continuous and closed sesquilinear forms on the Hilbert space H=L 2(Ω, μ). Denote by T=T(t) t≧0and S=S(t) t≧0the 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 t≧0 and fH. The method proposed uses ideas on invariance of closed convex sets of H under semigroups. Applications to elliptic operators and concrete examples are given.