Abstract
By the term classical sequence space we shall mean the spaces l p (ℕ, ℝ), c(ℕ, ℝ), and c 0(ℕ, ℝ) and their complex analogues. In section 12 we briefly develop the notion of a Schauder basis and study these bases in classical sequence spaces. In particular, we use basis theory to show that each infinite dimensional complemented subspace of a classical sequence space X is linearly isomorphic to X and that each infinite dimensional closed subspace of X contains an infinite dimensional complemented subspace.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Lacey, H.E. (1974). Classical Sequence Spaces. In: The Isometric Theory of Classical Banach Spaces. Die Grundlehren der mathematischen Wissenschaften, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65762-7_4
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DOI: https://doi.org/10.1007/978-3-642-65762-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65764-1
Online ISBN: 978-3-642-65762-7
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