Abstract
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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© 2011 Birkhäuser Boston
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Heil, C. (2011). Unconditional Bases in Banach Spaces. In: A Basis Theory Primer. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4687-5_6
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DOI: https://doi.org/10.1007/978-0-8176-4687-5_6
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4686-8
Online ISBN: 978-0-8176-4687-5
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