Geodesic
The space of real-analytic functions has no basis
Studia Mathematica, Tome 142 (2000) no. 2, pp. 187-200

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-142-2-187-200
Keywords: LB-space, Fréchet space, Schauder basis, Köthe sequence space, complemented subspace, space of real-analytic functions

Paweł Domański 1 ; Dietmar Vogt 1

1 
@article{10_4064_sm_142_2_187_200,
     author = {Pawe{\l} Doma\'nski and Dietmar Vogt},
     title = {The space of real-analytic functions has no basis},
     journal = {Studia Mathematica},
     pages = {187--200},
     publisher = {mathdoc},
     volume = {142},
     number = {2},
     year = {2000},
     doi = {10.4064/sm-142-2-187-200},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-142-2-187-200/}
}
TY  - JOUR
AU  - Paweł Domański
AU  - Dietmar Vogt
TI  - The space of real-analytic functions has no basis
JO  - Studia Mathematica
PY  - 2000
SP  - 187
EP  - 200
VL  - 142
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-142-2-187-200/
DO  - 10.4064/sm-142-2-187-200
LA  - en
ID  - 10_4064_sm_142_2_187_200
ER  - 
%0 Journal Article
%A Paweł Domański
%A Dietmar Vogt
%T The space of real-analytic functions has no basis
%J Studia Mathematica
%D 2000
%P 187-200
%V 142
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-142-2-187-200/
%R 10.4064/sm-142-2-187-200
%G en
%F 10_4064_sm_142_2_187_200
Paweł Domański; Dietmar Vogt. The space of real-analytic functions has no basis. Studia Mathematica, Tome 142 (2000) no. 2, pp. 187-200. doi: 10.4064/sm-142-2-187-200

Cité par Sources :