Basic sequences and norming subspaces in non-quasi-reflexive Banach spaces |
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Authors: | William J Davis William B Johnson |
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Institution: | (1) The Ohio State University, 43210 Colombus, Ohio, U.S.A. |
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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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