Norm-attaining operators into strictly convex Banach spaces
Bishop and Phelps proved in 1961 that the set of scalar valued norm attaining bounded linear operators on any Banach space \(X\) is dense in \(X^*\). The author considers here the problem of extending this result to one in which the scalar field is replaced by a more general Banach space \(Y\), showing that if \(Y\) is strictly convex and contains a certain type of basic sequence, then there exists a Banach space \(X\) for which the norm attaining operators from \(X\) to \(Y\) are not dense. A corollary is that no uniformly convex Banach space has Property B of Lindenstrauss.
scientific article; zbMATH DE number 1218611
scientific article