Isometric embedding into spaces of continuous functions

• Autorzy: Rafael Villa
• Języki publikacji: EN

Abstrakty

EN

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 $C_0(β+1)$.

Słowa kluczowe

EN

metric space; Banach space; metric linear dimension

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 3
• Strony: 197-205

Daty

wydano

1998

otrzymano

1996-11-12

poprawiono

1997-12-31

Twórcy

autor

Rafael Villa

• Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, c/Tarfia, s/n, 41012 Sevilla, Spain

Bibliografia

• [1] S. Banach, Théorie des opérations linéaires, Chelsea, New York, 1933.
• [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.
• [5] S. Mazur et S. Ulam, Sur les transformations isométriques d'espaces vectoriels normés, C. R. Acad. Sci. Paris 194 (1932), 946-948.
• [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.