On isometrical extension properties of function spaces
Commentationes Mathematicae Universitatis Carolinae (2015)
- Volume: 56, Issue: 1, page 105-115
- ISSN: 0010-2628
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topKato, Hisao. "On isometrical extension properties of function spaces." Commentationes Mathematicae Universitatis Carolinae 56.1 (2015): 105-115. <http://eudml.org/doc/269887>.
@article{Kato2015,
abstract = {In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces $C(Q)$ and $C(\Delta )$, where $Q$ and $\Delta $ denote the Hilbert cube $[0,1]^\{\infty \}$ and a Cantor set, respectively.},
author = {Kato, Hisao},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear extension of isometry; theorem of Banach and Mazur; Hilbert cube; Cantor set; separable metric space; surjective isometry; isometric embedding; function space; linear extension of isometry; Hilbert cube; Cantor set},
language = {eng},
number = {1},
pages = {105-115},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On isometrical extension properties of function spaces},
url = {http://eudml.org/doc/269887},
volume = {56},
year = {2015},
}
TY - JOUR
AU - Kato, Hisao
TI - On isometrical extension properties of function spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 1
SP - 105
EP - 115
AB - In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces $C(Q)$ and $C(\Delta )$, where $Q$ and $\Delta $ denote the Hilbert cube $[0,1]^{\infty }$ and a Cantor set, respectively.
LA - eng
KW - linear extension of isometry; theorem of Banach and Mazur; Hilbert cube; Cantor set; separable metric space; surjective isometry; isometric embedding; function space; linear extension of isometry; Hilbert cube; Cantor set
UR - http://eudml.org/doc/269887
ER -
References
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