Banach空间中非交换非线性拓扑半群的遍历压缩定理

Ergodic Retraction Theorem for Noncommutative and Nonlinear Topological Semigroups in Banach Spaces

在具Frechet可微范数的实自反Banach空间中,给出渐近非扩张型半群的殆渐近等距的殆轨道的遍历压缩定理,即设C是具(F)可微范数的实自反Banach空间X的有界凸闭子集,G是右可逆拓扑半群,S是C上(Γ)类渐近非扩张型半群,若D有不变平均。

This paper gives ergodic retraction theorem for almost asymptotically isometric orbits of asymptotically nonexpansive type semigroups in a real reflexive Banach space with a Frechet differentiable norm. Let C be a bounded closed convex subset of a real reflexive Banach space X with a Frechet differentiable norm and G be a right reversible topological semigroup. S is an asymptotically nonexpansive type semigroup which is of type（F） acting on C. If D has an invariant mean, there will exist a nonexpansive retraction P.