Classical Sequence Spaces
By the term classical sequence space we shall mean the spaces l p (ℕ, ℝ), c(ℕ, ℝ), and c0(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.
KeywordsBanach Space Bound Linear Operator Basic Sequence Separable Banach Space Compact Hausdorff Space
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