赋Orlicz范数的Orlicz序列空间的局部k-β性质

Partial property(k-β) of Orlicz sequence spaces equipped withthe Orlicz norm

β点是Banach空间中一类重要的点态性质,关于它在Banach空间的研究已经相对完善.2019年k-β点的定义被提出,k-β点的定义是在β点的定义基础上进行推广得出来的,至今关于k-β性质的研究还很少,因此着重研究了k-β点在一类具体的Banach空间—赋Orlicz范数的Orlicz序列空间中的具体刻画,然后作为推论给出了这个空间具有局部k-β性质的判别条件.

β point is an important type of point-state property in Banach spaces.The research on it in Banachspaces has been relatively completed.In 2019,the definition of k-β point was proposed.The definition of k-β point is derived from the definition of β point.So far there is very little research on k-β properties.A criteria of k-β point in Orlicz sequence spaces equipped with the Orlicz norm was given,and then we got the equivalent condition for property (k-β) of these spaces.