On démontre un théorème facile concernant une condition suffisante pour que la somme de deux sous-espaces fermés d’un espace de Banach soit fermée. Ce théorème conduit à plusieurs résultats du type du théorème de Sarason, qui dit que
A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that
@article{AIF_1975__25_1_99_0, author = {Rudin, Walter}, title = {Spaces of type $H^\infty +C$}, journal = {Annales de l'Institut Fourier}, pages = {99--125}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {25}, number = {1}, year = {1975}, doi = {10.5802/aif.545}, mrnumber = {51 #13692}, zbl = {0295.46080}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.545/} }
Rudin, Walter. Spaces of type $H^\infty +C$. Annales de l'Institut Fourier, Tome 25 (1975) no. 1, pp. 99-125. doi : 10.5802/aif.545. http://archive.numdam.org/articles/10.5802/aif.545/
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