# Isometric embedding into spaces of continuous functions

Studia Mathematica (1998)

- Volume: 129, Issue: 3, page 197-205
- ISSN: 0039-3223

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topVilla, Rafael. "Isometric embedding into spaces of continuous functions." Studia Mathematica 129.3 (1998): 197-205. <http://eudml.org/doc/216500>.

@article{Villa1998,

abstract = {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 $C_0(α+1)$ and $C_0(β+1)$.},

author = {Villa, Rafael},

journal = {Studia Mathematica},

keywords = {metric space; Banach space; metric linear dimension; isometric embedding},

language = {eng},

number = {3},

pages = {197-205},

title = {Isometric embedding into spaces of continuous functions},

url = {http://eudml.org/doc/216500},

volume = {129},

year = {1998},

}

TY - JOUR

AU - Villa, Rafael

TI - Isometric embedding into spaces of continuous functions

JO - Studia Mathematica

PY - 1998

VL - 129

IS - 3

SP - 197

EP - 205

AB - 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 $C_0(α+1)$ and $C_0(β+1)$.

LA - eng

KW - metric space; Banach space; metric linear dimension; isometric embedding

UR - http://eudml.org/doc/216500

ER -

## References

top- [1] S. Banach, Théorie des opérations linéaires, Chelsea, New York, 1933. Zbl0067.08902
- [2] C. Bessaga and A. Pełczyński, Spaces of continuous functions (IV), Studia Math. 19 (1960), 53-62.
- [3] R. Engelking, General Topology, PWN, Warszawa, 1977.
- [4] T. Figiel, On non-linear isometric embeddings of normed linear spaces, Bull. Acad. Polon. Sci. 16 (1968), 185-188. Zbl0155.18301
- [5] S. Mazur et S. Ulam, Sur les transformations isométriques d'espaces vectoriels normés, C. R. Acad. Sci. Paris 194 (1932), 946-948. Zbl58.0423.01
- [6] S. Rolewicz, Metric Linear Spaces, Reidel and PWN, Dordrecht and Warszawa, 1985.
- [7] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa, 1971.
- [8] W. Sierpiński, Cardinal and Ordinal Numbers, PWN, Warszawa, 1958.

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