论文标题
$ l^p $和$ \ mathcal {c}（k）$的增长率最终为正kreiss限制$ C_0 $ -Semigroups
Growth rate of eventually positive Kreiss bounded $C_0$-semigroups on $L^p$ and $\mathcal{C}(K)$
论文作者
论文摘要
在本文中，我们比较了Banach空间上的$ C_0 $ -Semigroup的几个Cesàro和Kreiss型有界条件，我们表明这些条件与Banach Lattice上的正面半群相当。此外，我们对某些Banach Lattices $ x $的Kreiss有限且最终为正的$ C_0 $ -Semigroup $（T_T）_ {T \ GE 0} $的增长率估计。我们证明，如果$ x $是$ l^p $ -space，$ 1 <p <+\ infty $，则$ \ | t_t \ | = \ Mathcal {o} \ left（t/\ log（t）^{\ max（1/p，1/p，1/p'）} \ right）$，如果$ x $是$（\ text {al}）$或$（\ text {am}） $ε\ in（0,1）$，改善了先前的估计。
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 $(T_t)_{t\ge 0}$ on certain Banach lattices $X$. We prove that if $X$ is an $L^p$-space, $1<p<+\infty$, then $\|T_t\| = \mathcal{O}\left(t/\log(t)^{\max(1/p,1/p')}\right)$ and if $X$ is an $(\text{AL})$ or $(\text{AM})$-space, then $\|T_t\|=\mathcal{O}(t^{1-ε})$ for some $ε\in (0,1)$, improving previous estimates.
