Banach空间中的逼近问题

The Approximation Problem and Differentiability of the Norm in Banach Spaces

说明了三种类型的Ｂａｎａｃｈ空间都存在不具有（β）性质的可逼近集，指出在等价范数的意义下，每个具基的Ｂａｎａｃｈ空间都存在不具有（β）性质的可逼近集．此外还讨论了Ｂａｎａｃｈ空间中的可逼近集具有（β）性质的条件．

In this paper,It Is shownthat three types Banachspace there are proximinal sets which lacks property(β).And proses that for every Infinite-dimensional Banach space with a basis there exists an equlvakat norm such that there exists a proximinal set without property(β).In addition,discusses the conditions of proximinal sets which has property(β)on Banach space.