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- W4313422589 abstract "In this paper, we compare several Cesàro- and Kreiss-type boundedness conditions for a $$C_0$$ -semigroup on a Banach space and we show that those conditions are all equivalent for a positive semigroup on a Banach lattice. Furthermore, we give an estimate of the growth rate of a Kreiss bounded and eventually positive $$C_0$$ -semigroup $$(T_t)_{tge 0}$$ on certain Banach lattices X. We prove that if X is an $$L^p$$ -space, $$1<p<+infty $$ , then $$Vert T_tVert = mathcal {O}left( t/log (t)^{max (1/p,1/p')}right) $$ , and if X is an $$(text {AL})$$ or $$(text {AM})$$ -space, then $$Vert T_tVert =mathcal {O}(t^{1-epsilon })$$ for some $$epsilon in (0,1)$$ , improving previous estimates." @default.
- W4313422589 created "2023-01-06" @default.
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- W4313422589 date "2022-12-19" @default.
- W4313422589 modified "2023-10-13" @default.
- W4313422589 title "Growth rate of eventually positive Kreiss bounded $$C_0$$-semigroups on $$L^p$$ and $$mathcal {C}(K)$$" @default.
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- W4313422589 doi "https://doi.org/10.1007/s00028-022-00860-0" @default.
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