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Classical Sequence Spaces

  • H. Elton Lacey
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 208)

Abstract

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.

Keywords

Banach Space Bound Linear Operator Basic Sequence Separable Banach Space Compact Hausdorff Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1974

Authors and Affiliations

  • H. Elton Lacey
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

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