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The space of real-analytic functions has no basis

Paweł Domański; Dietmar Vogt

Studia Mathematica (2000)

  • Volume: 142, Issue: 2, page 187-200
  • ISSN: 0039-3223

Abstract

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Let Ω be an open connected subset of d . 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.

How to cite

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Domański, Paweł, and Vogt, Dietmar. "The space of real-analytic functions has no basis." Studia Mathematica 142.2 (2000): 187-200. <http://eudml.org/doc/216797>.

@article{Domański2000,
abstract = {Let Ω be an open connected subset of $ℝ^d$. 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.},
author = {Domański, Paweł, Vogt, Dietmar},
journal = {Studia Mathematica},
keywords = {LB-space; Fréchet space; Schauder basis; Köthe sequence space; complemented subspace; space of real-analytic functions; metrizable complemented subspaces; PLN-space; LN-space; LB-spaces; nuclear linking maps; Schauder bases; ultrabornological PLN-space; property ; property (DN); complemented Fréchet subspace},
language = {eng},
number = {2},
pages = {187-200},
title = {The space of real-analytic functions has no basis},
url = {http://eudml.org/doc/216797},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Domański, Paweł
AU - Vogt, Dietmar
TI - The space of real-analytic functions has no basis
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 2
SP - 187
EP - 200
AB - Let Ω be an open connected subset of $ℝ^d$. 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.
LA - eng
KW - LB-space; Fréchet space; Schauder basis; Köthe sequence space; complemented subspace; space of real-analytic functions; metrizable complemented subspaces; PLN-space; LN-space; LB-spaces; nuclear linking maps; Schauder bases; ultrabornological PLN-space; property ; property (DN); complemented Fréchet subspace
UR - http://eudml.org/doc/216797
ER -

References

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