A Schauder basis provides unique series representations of each vector in a Banach space. However, conditionally convergent series are delicate in many respects. For example, if converges conditionally and is a bounded sequence of scalars, P then the series may not converge. Unconditionality is an important property,and in many applications we greatly prefer a basis that is unconditional over one that is conditional. Therefore we study unconditional bases in more detail in this chapter.

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1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

   Christopher Heil

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Correspondence toChristopher Heil.

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