一个矢值序列赋值收敛定理

A vector-valued sequential-evaluation convergence theorem

对于一类经典的矢值序列空间,引入一类重要子集,它包括该序列空间的全部全有界集和许多非全有界集。得到该集族的一些重要性质,获得了一个矢值序列赋值收敛定理,从而揭示了映射级数矢值序列赋值收敛的更强内涵。结论完全去掉了通常对映射的线性限制,应用前景扩大。

For a type of classic vector - valued sequence space, a class of important subsets is introduced. It ineludes all totally bounded sets and many sets which are not totally bounded in the sequence space. Some important properties of the subset family have been found. A vector - valued sequential - evaluation convergence theorem is obtained, from which stronger intrinsic meaning of vector - valued sequential - evaluation convergence of mapping series is promulgated. Conclusion completely drop the linearity restriction forced on the mappings as usual and is an obvious extension for applications in future.