We prove that some Banach spaces X have the property that every Banach space that can be isometrically embedded in X can be isometrically and linearly embedded in X. We do not know if this is a general property of Banach spaces. As a consequence we characterize for which ordinal numbers α, β there exists an isometric embedding between and .
@article{bwmeta1.element.bwnjournal-article-smv129i3p197bwm,
author = {Rafael Villa},
title = {Isometric embedding into spaces of continuous functions},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {197-205},
zbl = {0915.46007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv129i3p197bwm}
}
Villa, Rafael. Isometric embedding into spaces of continuous functions. Studia Mathematica, Tome 129 (1998) pp. 197-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv129i3p197bwm/
[00000] [1] S. Banach, Théorie des opérations linéaires, Chelsea, New York, 1933. | Zbl 0067.08902
[00001] [2] C. Bessaga and A. Pełczyński, Spaces of continuous functions (IV), Studia Math. 19 (1960), 53-62.
[00002] [3] R. Engelking, General Topology, PWN, Warszawa, 1977.
[00003] [4] T. Figiel, On non-linear isometric embeddings of normed linear spaces, Bull. Acad. Polon. Sci. 16 (1968), 185-188. | Zbl 0155.18301
[00004] [5] S. Mazur et S. Ulam, Sur les transformations isométriques d'espaces vectoriels normés, C. R. Acad. Sci. Paris 194 (1932), 946-948. | Zbl 58.0423.01
[00005] [6] S. Rolewicz, Metric Linear Spaces, Reidel and PWN, Dordrecht and Warszawa, 1985.
[00006] [7] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa, 1971.
[00007] [8] W. Sierpiński, Cardinal and Ordinal Numbers, PWN, Warszawa, 1958.