Embeddings of C(K) spaces into C(S,X) spaces with distortion strictly less than 3

• Autorzy: Leandro Candido , Elói Medina Galego
• Języki publikacji: EN

Abstrakty

EN

In the spirit of the classical Banach-Stone theorem, we prove that if K and S are intervals of ordinals and X is a Banach space having non-trivial cotype, then the existence of an isomorphism T from C(K, X) onto C(S,X) with distortion $||T|| ||T^{-1}||$ strictly less than 3 implies that some finite topological sum of K is homeomorphic to some finite topological sum of S. Moreover, if Xⁿ contains no subspace isomorphic to $X^{n+1}$ for every n ∈ ℕ, then K is homeomorphic to S. In other words, we obtain a vector-valued Banach-Stone theorem which is an extension of a Gordon theorem and at the same time an improvement of a Behrends and Cambern theorem. In order to prove this, we show that if there exists an embedding T of a C(K) space into a C(S,X) space, with distortion strictly less than 3, then the cardinality of the αth derivative of S is finite or greater than or equal to the cardinality of the αth derivative of K, for every ordinal α.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 220
• Numer: 1
• Strony: 83-92

Daty

wydano

2013

Twórcy

autor

Leandro Candido

• Department of Mathematics, IME, University of São Paulo, Rua do Matão 1010, São Paulo, Brazil

autor

Elói Medina Galego

• Department of Mathematics, IME, University of São Paulo, Rua do Matão 1010, São Paulo, Brazil

Identyfikatory

DOI

10.4064/fm220-1-5