On Summable Bases in Banach Spaces
Mangatiana A. Robderai *
Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.
*Author to whom correspondence should be addressed.
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.
Keywords: Unconditional bases, unconditional convergence, Dvoretski-Rogers Theorem, bounded approximation, finite dimensional decomposition