The Journal of the Indian Mathematical Society

P. K. Jain ¹, S. K. Kaushik ¹

Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, IN

Abstract

Banach [2] considered M-bases which, in fact he called ‘complete biorthogonal system’. Markushevic [12] observed that these bases are available in every separable Banach space, while it is now known that bases may not exist in every separable Banach space [8].

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P. K. Jain ¹, K. K. Arora ², D. P. Sinha ³

Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, IN
2 Department of Mathematics, Rajdhani College, (University of Delhi), Ring Road, Raja Garden, New Delhi-110015, IN
3 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 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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