局部凸空间中的不动点性质和Q-非扩张收缩
Fixed point properties and Q-nonexpansive retractions in locally convex spaces
摘要：
设Q是局部凸空间E上的一个赋范族，它决定了E的拓扑.研究了Q-非扩张映射族的Q-非扩张收缩的存在性，证明了具有弱不动点性质的分离的序列完备局部凸空间$E$对Q-非扩张映射族的可交换可分拓扑半群也具有弱不动点性质.这证明了[5]中关于局部凸空间的Bruck问题。此外，我们证明了右顺从Q-非扩张半群的Q-非扩张收缩的存在性。
英文摘要：
Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially complete locally convex space $E$ that has the weak fixed point property, has the weak fixed point property for commuting separable semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck's problem [5] for locally convex spaces. Moreover, we prove the existence of Q-nonexpansive retractions for the right amenable Q-nonexpansive semigroups.
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