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.
CITATION STYLE
Heil, C. (2011). Unconditional Bases in Banach Spaces. In Applied and Numerical Harmonic Analysis (pp. 177–188). Springer International Publishing. https://doi.org/10.1007/978-0-8176-4687-5_6
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