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    徐洪坤. 可逆Lipschitz半群的弱收敛性[J]. 华东理工大学学报(自然科学版), 1991, (4).
    引用本文: 徐洪坤. 可逆Lipschitz半群的弱收敛性[J]. 华东理工大学学报(自然科学版), 1991, (4).
    Xu Hongkun. Weak Convergence for Reversible Lipschitzian Semigroups[J]. Journal of East China University of Science and Technology, 1991, (4).
    Citation: Xu Hongkun. Weak Convergence for Reversible Lipschitzian Semigroups[J]. Journal of East China University of Science and Technology, 1991, (4).

    可逆Lipschitz半群的弱收敛性

    Weak Convergence for Reversible Lipschitzian Semigroups

    • 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。

       

      Abstract: 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.

       

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