Abstract
Let X be an infinite-dimensional normed linear space. A sequence \(\left\{ {{e_i}} \right\}_i^\infty = 1\) in X is called a Schauder basis of X if for every x ∈ X there is a unique sequence of scalars \(\left( {{a_i}} \right)_i^\infty = 1\) called the coordinates of x, such that \(x = \sum\limits_{i = 1}^\infty {{a_i}{e_i}}\).
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© 2001 Springer Science+Business Media New York
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Fabian, M., Habala, P., Hájek, P., Santalucía, V.M., Pelant, J., Zizler, V. (2001). Schauder Bases. In: Functional Analysis and Infinite-Dimensional Geometry. Canadian Mathematical Society / Société mathématique du Canada. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3480-5_6
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DOI: https://doi.org/10.1007/978-1-4757-3480-5_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2912-9
Online ISBN: 978-1-4757-3480-5
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