Abstract
A Banach spaceX is non-quasi-reflexive (i.e. dimX **/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 allk. A basic sequence which is non-k-shrinking for allk exists inX if and only ifX * contains a norming subspace of infinite codimension. This need not occur even ifX is non-quasi-reflexive. Every norming subspace ofX * has finite codimension if and only if for every normingM inX *, everyM-closedY inX,M∩Y T is norming overX/Y. This solves a problem due to Schäffer [19].
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The second-named author was supported in part by NSF GP 28719.
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Davis, W.J., Johnson, W.B. Basic sequences and norming subspaces in non-quasi-reflexive Banach spaces. Israel J. Math. 14, 353–367 (1973). https://doi.org/10.1007/BF02764714
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DOI: https://doi.org/10.1007/BF02764714