Basic sequences and norming subspaces in non-quasi-reflexive Banach spaces

A Banach space X is non-quasi-reflexive (i.e. dim X **/X=) if and only if it contains a basic sequence spanning a non-quasi-reflexive subspace. In fact, this basic sequence can be chosen to be non-k-boundedly complete for all k. A basic sequence which is non-k-shrinking for all k exists in X if and only if X * contains a norming subspace of infinite codimension. This need not occur even if X is non-quasi-reflexive. Every norming subspace of X * has finite codimension if and only if for every norming M in X *, every M-closed Y in X, MY T is norming over X/Y. This solves a problem due to Schffer [19]. 1973 Hebrew University.

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