乘积空间球覆盖性质的稳定性
发布时间：2018-09-17 13:56
【摘要】：假设(33)是Banach空间X中由闭球(或开球)所构成的球簇,如果每个球都不包含原点,并且所有球的并覆盖了X的单位球面XS,则称(33)是X的一个球覆盖.如果X存在一个由可数多个球所构成的球覆盖,则称X具有球覆盖性质(ball-covering property,简写为BCP).文献]1[证明了:对于Gateaux可微空间(GDS)X和Y,它们具有BCP当且仅当它们的乘积空间(?),具有BCP,其中(?)本文没有GDS的条件下,证明了,对于Banach空间X与Y,它们具有BCP当且仅当X×Y在范数(?)具有BCP,其中1≤p≤∞.其次,我们把有限乘积空间的BCP问题推广到无限乘积,也就是说,如果X_k是具有BCP的Banach空间,则(?)也具有BCP,其中k∈N,1≤p≤∞。
[Abstract]:Suppose (33) is a cluster of closed balls (or tee balls) in Banach space X, if each ball does not contain the origin, and the unit sphere XS, of all balls and covering X is called (33) a ball cover of X. If X has a ball covering consisting of countable balls, then X has the property of ball covering (ball-covering property, abbreviated as BCP). [it is proved that for Gateaux differentiable spaces (GDS) X and Y, they have BCP if and only if their product spaces (?) and BCP, spaces (?) In this paper, we prove that for Banach spaces X and Y, they have BCP if and only if X 脳 Y is in the norm (?) We have BCP, where 1 鈮，
本文编号：2246139
[Abstract]:Suppose (33) is a cluster of closed balls (or tee balls) in Banach space X, if each ball does not contain the origin, and the unit sphere XS, of all balls and covering X is called (33) a ball cover of X. If X has a ball covering consisting of countable balls, then X has the property of ball covering (ball-covering property, abbreviated as BCP). [it is proved that for Gateaux differentiable spaces (GDS) X and Y, they have BCP if and only if their product spaces (?) and BCP, spaces (?) In this paper, we prove that for Banach spaces X and Y, they have BCP if and only if X 脳 Y is in the norm (?) We have BCP, where 1 鈮，
本文编号：2246139
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