On Summable Bases in Banach Spaces

Mangatiana A. Robderai

doi:10.9734/BJMCS/2014/11589

Research Article Open access CC BY 3.0

On Summable Bases in Banach Spaces

Mangatiana A. Robderai

Journal of Advances in Mathematics and Computer Science · pp. 2361–2372 · Published 24 Jun 2014

10.9734/BJMCS/2014/11589

Abstract

We introduce the notion of summable bases that naturally generalizes the notion of unconditional sequence bases for Banach spaces. We shall be particularly interested in some classical results on sequences and series in separable Banach spaces that carry over or naturally extend to the case of non-separable Banach spaces.

Unconditional bases unconditional convergence Dvoretski-Rogers Theorem bounded approximation finite dimensional decomposition

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Mangatiana A. Robderai (2014). On Summable Bases in Banach Spaces. Journal of Advances in Mathematics and Computer Science , 2361–2372. https://doi.org/10.9734/BJMCS/2014/11589

Affiliations

Mangatiana A. Robderai — Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.

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