Abstract
In this paper—which is a continuation of [10]—we exhibit some topological conditions on a Banach space which ensure that it contains isometric copies of infinite-dimensional conjugate spaces. This result is used to identify a large class of Banach spaces that are hereditarily separable duals. A method of defining a “Jamestree sum” of a countable number of Banach spaces is given. It is used to construct various counterexamples; for instance, there exists for each integer n a Banach space that can be mapped into Hilbert space via the composition of n but not ( n − 1) G δ-embeddings. We also continue the investigation of the global structure of some geometrically defined Banach spaces. For example, it is shown that a separable Banach space X with the Radon-Nikodym property (R.N.P.) has a subspace y with a boundedly complete finite-dimensional decomposition (F.D.D.) such that X Y has an F.D.D. and the R.N.P.
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