Weakly open sets in the unit ball of some Banach spaces and the centralizer
This paper adds to the knowledge of spaces in which every nonempty weakly open subset of the unit ball is of norm diameter 2. In this substantial contribution, the authors show that for any Banach space \(X\) with an infinite-dimensional centralizer, for any positive integer \(N\), the \(N\)-fold symmetric projective tensor product of \(X\), endowed with the symmetric projective norm, has this property. They also show that when \(X\) is non-reflexive with \(X^\ast\) \(L\)-embedded, the space generated by the duals of \(X\) of even order has an infinite-dimensional centralizer.
scientific article; zbMATH DE number 5757613
scientific article