Abstract
LetX be anL 1- orL 2-Banach lattice. Let (W(t)) t≥0 be aC 0-semigroup of positive operators onX with generator−T. Two examples ofC 0-semigroups are presented for which the identity\(e^{\sigma ( - T)t} = \sigma (W(t)) - \left\{ 0 \right\}\) fails for almost allt>0.
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Takac, P. Two counterexamples to the spectral mapping theorem for semigroups of positive operators. Integr equ oper theory 9, 460–467 (1986). https://doi.org/10.1007/BF01199354
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DOI: https://doi.org/10.1007/BF01199354