Examples of hereditarily<i>l</i>¹Banach spaces failing the Schur property

Abstract

A class of separable Banach sequence spaces is constructed. A member X of this class (i) is a hereditarily I 1 dual space which fails the Schur property, and (ii) is of codimension one in its first Baire class. A consequence of (ii) is that X is not isomorphic to the square of any Banach space Y.