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Kato's equality and spectral decomposition for positive C0-groups

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Abstract

Let A be the generator of a C0-semigroup {T(t); t⩾0} defined on a Banach lattice E. It is shown that T(t) is a lattice homomorphism for all t>0 if and only if A satisfies <¦x¦, A′x′>=<sign q(x)Ax, x′> (x∈D(A), x′ ∈D(A′)) (where q: E→E” is the evaluation mapping). This equality is used to obtain a spectral decomposition for generators of positive groups.

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  1. Mathematisches Institut der Universität, Auf der Morgenstelle 10, D-7400, Tübingen 1

    Wolfgang Arendt

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  1. Wolfgang Arendt
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Arendt, W. Kato's equality and spectral decomposition for positive C0-groups. Manuscripta Math 40, 277–298 (1982). https://doi.org/10.1007/BF01174880

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