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

Abstract

For a Banach space E of density equal to the cardinality of the smallest uncountable ordinal number Ï‰1 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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Published

1999-12-01

How to Cite

Jain, P. K., Arora, K. K., & Sinha, D. P. (1999). On Banach Spaces of the Smallest Uncountable Density With PRI. The Journal of the Indian Mathematical Society, 66(1-4), 185–191. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/21989

Issue

Volume 66, Issue 1-4, January-December 1999

Section

Articles

License

Copyright (c) 1999 P. K. Jain, K. K. Arora, D. P. Sinha

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.