Two applications of smoothness in C(K) spaces

• Autorzy: Matías Raja
• Języki publikacji: EN

Abstrakty

EN

A simple observation about embeddings of smooth Banach spaces into C(K) spaces allows us to construct a parametrization of the separable Banach spaces using closed subsets of the interval [0,1]. The same idea is applied to the study of the isometric embedding of $ℓ_{p}$ spaces into certain C(K) spaces with the additional condition that the functions of the image must be Lipschitz with respect to a fixed finer metric on K. The feasibility of that kind of embeddings is related to Szlenk indices.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 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: 2014
• Tom: 225
• Numer: 1
• Strony: 1-7

Daty

wydano

2014

Twórcy

autor

Matías Raja

• Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain

Identyfikatory

DOI

10.4064/sm225-1-1