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ON FRAME SYSTEMS IN BANACH SPACES

P. K. JAIN

Department of Mathematics, University of Delhi, Delhi 110 007, India

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S. K. KAUSHIK

Department of Mathematics, Kirorimal College (University of Delhi), Delhi 110 007, India

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, and

NISHA GUPTA

Department of Mathematics, University of Delhi, Delhi 110 007, India

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https://doi.org/10.1142/S021969130900274XCited by:3 (Source: Crossref)

Abstract

Banach frame systems in Banach spaces have been defined and studied. A sufficient condition under which a Banach space, having a Banach frame, has a Banach frame system has been given. Also, it has been proved that a Banach space E is separable if and only if E* has a Banach frame ({φ_n},T) with each φ_n weak*-continuous. Finally, a necessary and sufficient condition for a Banach Bessel sequence to be a Banach frame has been given.

Keywords:

AMSC: 42C15, 42A38

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