On Ball Dentable Property in Banach Spaces
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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 rentability 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 \(X^*\) has the \(w^*\)-Ball dentable property.
KeywordsSlices M-Ideals Strict ideals