Let Ω be an open connected subset of . 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.
@article{bwmeta1.element.bwnjournal-article-smv142i2p187bwm,
author = {Pawe\l\ Doma\'nski and Dietmar Vogt},
title = {The space of real-analytic functions has no basis},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {187-200},
zbl = {0990.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p187bwm}
}
Domański, Paweł; Vogt, Dietmar. The space of real-analytic functions has no basis. Studia Mathematica, Tome 141 (2000) pp. 187-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p187bwm/
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