Points of weak*-norm continuity in the dual unit ball of injective tensor product spaces (Q1566948)

The author continues his investigation of points in the dual unit ball \(B(Z^*)\) of a Banach space \(Z\) where the identity map of \(B(Z^*)\) is weak\(^*\)-norm continuous. In the case of spaces of continuous functions \(Z=C(K,X)\) where \(K\) is compact, a description has been given by \textit{Z.-B. Hu} and \textit{M. A. Smith} [Lect. Notes Pure Appl. Math. 172, 205-222 (1995; Zbl 0844.46018)]. In the more general case where \(Z=Y\otimes_\varepsilon X\) and \(Y\) is a \(G\)-space, the author contributes an extended version for the construction of points of weak\(^*\)-norm continuity (leaving open if this gives all such points). There are also results on strongly extreme points of \(B((Y\otimes_\varepsilon X)^*)\).