Isometric embedding into spaces of continuous functions

Rafael Villa

Studia Mathematica (1998)

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

Abstract

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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 ) .

How to cite

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Villa, 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

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  1. [1] S. Banach, Théorie des opérations linéaires, Chelsea, New York, 1933. Zbl0067.08902
  2. [2] C. Bessaga and A. Pełczyński, Spaces of continuous functions (IV), Studia Math. 19 (1960), 53-62. 
  3. [3] R. Engelking, General Topology, PWN, Warszawa, 1977. 
  4. [4] T. Figiel, On non-linear isometric embeddings of normed linear spaces, Bull. Acad. Polon. Sci. 16 (1968), 185-188. Zbl0155.18301
  5. [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. [6] S. Rolewicz, Metric Linear Spaces, Reidel and PWN, Dordrecht and Warszawa, 1985. 
  7. [7] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa, 1971. 
  8. [8] W. Sierpiński, Cardinal and Ordinal Numbers, PWN, Warszawa, 1958. 

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