标题： 论巴拿赫空间中的球可纹性 显示英文标题

标题： On Ball Dentable Property in Banach Spaces

摘要： 在本工作中，我们引入了巴拿赫空间中的球形可去性质。我们研究了$w^*$-球形可去性质的一些稳定性结果，从而在巴拿赫空间理想背景下讨论了球形可去性。我们证明了$w^*$-球形可去性质可以从$M$-理想提升到整个巴拿赫空间。我们还证明了对于巴拿赫空间的严格理想有类似的结果。 我们注意到当$K$是离散的且$X^\ast$具有$w^*$-Ball dentable 性质时，空间$C(K,X)^*$具有$w*$-Ball dentable 性质。 显示英文摘要

摘要： In this work, we introduce the notion of Ball dentable property in Banach spaces. We study certain stability results for the $w^*$-Ball dentable property leading to a discussion on Ball dentability in the context of ideals of Banach spaces. We prove that the $w^*$-Ball-dentable property can be lifted from an $M$-ideal to the whole Banach Space. We also prove similar results for strict ideals of a Banach space. We note that the space $C(K,X)^*$ has $w*$-Ball dentable property when $K$ is dispersed and $X^\ast$ has the $w^*$-Ball dentable property.