A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces

Antonio Moreno Galindo, and Ángel Rodríguez Palacios. "A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces." Studia Mathematica 166.1 (2005): 83-91. <http://eudml.org/doc/286547>.

@article{AntonioMorenoGalindo2005,
abstract = {We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ 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.},
author = {Antonio Moreno Galindo, Ángel Rodríguez Palacios},
journal = {Studia Mathematica},
language = {eng},
number = {1},
pages = {83-91},
title = {A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces},
url = {http://eudml.org/doc/286547},
volume = {166},
year = {2005},
}

TY - JOUR
AU - Antonio Moreno Galindo
AU - Ángel Rodríguez Palacios
TI - A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces
JO - Studia Mathematica
PY - 2005
VL - 166
IS - 1
SP - 83
EP - 91
AB - We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ 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.
LA - eng
UR - http://eudml.org/doc/286547
ER -