The Journal of the Indian Mathematical Society

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On Banach Spaces of the Smallest Uncountable Density With PRI


Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, India
2 Department of Mathematics, Rajdhani College, (University of Delhi), Ring Road, Raja Garden, New Delhi-110015, India
3 Department of Mathematics, Dyal Singh College (University of Delhi), Lodi Road, New Delhi-110003, India
     

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For a Banach space E of density equal to the cardinality of the smallest uncountable ordinal number ω1 and having a projectional resolution of the identity (in short, PRI), it is proved that there is a norming subspace V of E* such that the unit bail of V is σ(V,E)-angelic. In addition, if the PRI is of a special type called type I, then an Odell-Rosenthal type characterization is obtained for the non-containment of a copy of l1 in E.
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  • On Banach Spaces of the Smallest Uncountable Density With PRI

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Authors

P. K. Jain
Department of Mathematics, University of Delhi, Delhi-110007, India
K. K. Arora
Department of Mathematics, Rajdhani College, (University of Delhi), Ring Road, Raja Garden, New Delhi-110015, India
D. P. Sinha
Department of Mathematics, Dyal Singh College (University of Delhi), Lodi Road, New Delhi-110003, India

Abstract


For a Banach space E of density equal to the cardinality of the smallest uncountable ordinal number ω1 and having a projectional resolution of the identity (in short, PRI), it is proved that there is a norming subspace V of E* such that the unit bail of V is σ(V,E)-angelic. In addition, if the PRI is of a special type called type I, then an Odell-Rosenthal type characterization is obtained for the non-containment of a copy of l1 in E.