摘要
讨论了一类Lipschitz半群的弱收敛性问题。在Hilbert空间中证明了弱渐近正则性隐含半群轨道的弱收敛性;而在具有Frechet可微范数的一致凸Banach空间中证明了渐近正则性隐含半群轨道的弱收敛性。本文还讨论了收缩核的存在性问题。
The weak convergence for a class of Lipschitzian semigroups is discussed. It is proved that in a Hilbert space the weak asymptotic regularity implies the weak convergence of the semigroup; while in a uniformly convex Banach space with a Frechet differentiable norm, the asymptotic regularity implies the weak convergence of the semigroup. The existence of a retract for the semigroup is also discussed.
关键词
半群
收敛性
群论
fixed point
convergence
semigroup
Hilbert space
uniformly convex normed space
