Extremal structure of the unit ball of \(L^ p(\mu,X)\)
The authors consider and investigate a subset \(K\) of a real Banach space \(X\) and an extreme point \((\text{ext }K)\), a strongly extreme point \((\text{str-ext }K)\), an exposed point of \(K\), a strongly exposed point of \(K\) and they also a weak\(^*\) exposed point of \(K\) and a weak\(^*\) strongly exposed point of \(K\), and also consider the spaces \(L^q(\mu,X^*)\), \(L^p(\mu,X)\), \(L^p(\mu,X)^*\), \(L^q(\mu_{f,q},X^*)\), \(B_{L^p(\mu,X)^*}\), \(S_{L^q(\mu,X^*)}\). This long and important paper contains 15 theorems in which there are given e.g. properties of weak\(^*\) strongly exposed points, weak\(^*\) exposed points and also representations of the dual space \(L^p(\mu,X)\) as spaces of certain weak\(^*\) measurable functions from \(\Omega\) to \(X^*\).
scientific article; zbMATH DE number 908592