Resolvent norm decay does not characterize norm continuity

被引：1
|
作者：
Matrai, Tamas [1 ]
机构：
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1053 Budapest, Hungary
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2008年 / 168卷 / 01期
关键词：
D O I：
10.1007/s11856-008-1054-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that there exists a reflexive Banach space (chi, parallel to.parallel to) and a strongly continuous semigroup (T(t))(t >= 0) with generator (A, D(A)) on (chi, parallel to.parallel to) such that lim(mu is an element of R,) (vertical bar mu vertical bar -> infinity) parallel to R(i mu, A)parallel to = 0 but (T(t))(t >= 0) is not eventually norm continuous. This answers a question of Amnon Pazy in the negative.
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页码：1 / 28
页数：28
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