Basic Linear Structure

Antonio J. Guirao, Vicente Montesinos and Václav Zizler
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Antonio J. Guirao: Universitat Politècnica de València, Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada
Vicente Montesinos: Universitat Politècnica de València, Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada
Václav Zizler: University of Alberta, Department of Mathematical and Statistical Sciences

Chapter Chapter 1 in Open Problems in the Geometry and Analysis of Banach Spaces, 2016, pp 1-35 from Springer

Abstract: Abstract A sequence {e i } i = 1 ∞ in a Banach space X is called a Schauder basis for X basis Schauder if for each x ∈ X there is a unique sequence of scalars {α i } i = 1 ∞ such that $$x =\sum _{ i=1}^{\infty }\alpha _{i}e_{i}$$ . If the convergence of this series is unconditional convergence unconditional for all x ∈ X (i.e., any rearrangement of it converges), we say that the Schauder basis is unconditional basis Schauder unconditional . This is equivalent to say that under any permutation $$\pi: \mathbb{N} \rightarrow \mathbb{N}$$ , the sequence {e π(i)} i = 1 ∞ is again a basis of X.

Keywords: Hilbert Space; Banach Space; Unconditional Basis; Separable Space; Convex Norm (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-33572-8_1

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