Distance near the origin between elements of a strongly continuous semigroup
Distance near the origin between elements of a strongly continuous semigroup
复制标题
强连续半群元素之间的原点附近距离
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
J. Esterle
中科院分区：
文献类型：
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作者：
J. Esterle
AbstractSet
$$ heta (s/t): = (s/t - 1)(t/s)^{frac{{s/t}}{{s/t - 1}}} = (s - t)frac{{t^{t/(s - t)} }}{{s^{s/(s - t)} }}$$
if 0<t<s. The key result of the paper shows that if (T (t))t>0 is a nontrivial strongly continuous quasinilpotent semigroup of bounded operators on a Banach space then there exists δ>0 such that ║T(t)-T(s)║>θ(s/t) for 0<t<s≤δ. Also if (T(t))t>0 is a strongly continuous semigroup of bounded operators on a Banach space, and if there exists η>0 and a continuous functiont→s(t) on [0, ν], satisfyings(0)=0, and such that 0<t<s(t) and ║T(t)-T(s(t))║<θ(s/t) fort∈(o, η], then the infinitesimal generator of the semigroup is bounded. Various examples show that these results are sharp.
AbstractSet
$$ heta (s/t): = (s/t - 1)(t/s)^{frac{{s/t}}{{s/t - 1}}} = (s - t)frac{{t^{t/(s - t)} }}{{s^{s/(s - t)} }}$$
if 0<t<s. The key result of the paper shows that if (T (t))t>0 is a nontrivial strongly continuous quasinilpotent semigroup of bounded operators on a Banach space then there exists δ>0 such that ║T(t)-T(s)║>θ(s/t) for 0<t<s≤δ. Also if (T(t))t>0 is a strongly continuous semigroup of bounded operators on a Banach space, and if there exists η>0 and a continuous functiont→s(t) on [0, ν], satisfyings(0)=0, and such that 0<t<s(t) and ║T(t)-T(s(t))║<θ(s/t) fort∈(o, η], then the infinitesimal generator of the semigroup is bounded. Various examples show that these results are sharp.