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Title

The space of real-analytic functions has no basis

Authors 1, 2

Affiliations

  1. Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
  2. FB Mathematik, Bergische Universität Wuppertal, Gauß str. 20, D-42097 Wuppertal, Germany

Abstract

Let Ω be an open connected subset of ℝd. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

Keywords

ENG
LB-space, Fréchet space, Schauder basis, Köthe sequence space, complemented subspace, space of real-analytic functions

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Additional information

http://matwbn.icm.edu.pl/ksiazki/sm/sm142/sm14226.pdf

Studia Mathematica
2000/142/2
Export to PBN, Opens in new tab
Pages:
187-200
Main language of publication
English
Received
2000-03-06
Published
2000
Exact and natural sciences