A bilinear version of Holsztyński's theorem on
isometries of $C(X)$-spaces
Studia Mathematica, Tome 166 (2005) no. 1, pp. 83-91
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that, for a compact metric space $X$ not reduced to a
point, the existence of a bilinear mapping $\diamond :C(X)\times
C(X)\to C(X)$ satisfying $\Vert f\diamond g\Vert =\Vert f\Vert\,
\Vert g\Vert $ for all $f,g\in C(X)$ is equivalent to the
uncountability of $X$. This is derived from a bilinear version of
Holsztyński's theorem [3]
on isometries of $C(X)$-spaces,
which is also proved in the paper.
Keywords:
prove compact metric space reduced point existence bilinear mapping diamond times satisfying vert diamond vert vert vert vert vert equivalent uncountability derived bilinear version holszty skis theorem nbsp isometries spaces which proved paper
Affiliations des auteurs :
Antonio Moreno Galindo 1 ; Ángel Rodríguez Palacios 1
@article{10_4064_sm166_1_6,
author = {Antonio Moreno Galindo and \'Angel Rodr{\'\i}guez Palacios},
title = {A bilinear version of {Holszty\'nski's} theorem on
isometries of $C(X)$-spaces},
journal = {Studia Mathematica},
pages = {83--91},
publisher = {mathdoc},
volume = {166},
number = {1},
year = {2005},
doi = {10.4064/sm166-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm166-1-6/}
}
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Antonio Moreno Galindo; Ángel Rodríguez Palacios. A bilinear version of Holsztyński's theorem on isometries of $C(X)$-spaces. Studia Mathematica, Tome 166 (2005) no. 1, pp. 83-91. doi: 10.4064/sm166-1-6
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