Two counterexamples to the spectral mapping theorem for semigroups of positive operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Two counterexamples to the spectral mapping theorem for semigroups of positive operators

Authors:	Takac Peter

Affiliation:	(1) School of Mathematics, University of Minnesota, 55455 Minneapolis, MN, U.S.A.

Abstract:	LetX be anL¹- orL²-Banach lattice. Let (W(t))_t0 be aC₀-semigroup of positive operators onX with generator–T. Two examples ofC₀-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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