Basis Sets in Banach Spaces

S. V. Konyagin () and Y. V. Malykhin ()
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S. V. Konyagin: Steklov Mathematical Institute, Russian Academy of Sciences
Y. V. Malykhin: Steklov Mathematical Institute, Russian Academy of Sciences

Chapter Chapter 23 in Nonlinear Analysis, 2012, pp 381-386 from Springer

Abstract: Abstract A set M in a linear normed space X over a field K (K=ℝ or K=ℂ) is called a basis set if every x∈X can be represented as a sum x=∑ k c k e k , where e k ∈M, e k ≠e l (k≠l), c k ∈K∖{0}, ∑ k denotes either $\sum_{k=1}^{\infty}$ or $\sum_{k=1}^{N}$ , and this representation is unique up to permutations. We prove the existence of an infinite-dimensional separable Banach space X with a basis set M such that no arrangement of M forms a Schauder basis.

Keywords: Basis; Schauder basis; Rearrangement; 46Bxx; 42A20; 39B52 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3498-6_23

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