On the number of non-isomorphic subspaces of a Banach space

• Autorzy: Valentin Ferenczi , Christian Rosendal
• Języki publikacji: EN

Abstrakty

EN

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let 𝔛 be a Banach space with an unconditional basis $(e_{i})_{i∈ℕ}$; then either there exists a perfect set P of infinite subsets of ℕ such that for any two distinct A,B ∈ P, $[e_{i}]_{i∈A} ≇ [e_{i}]_{i∈B}$, or for a residual set of infinite subsets A of ℕ, $[e_{i}]_{i∈A}$ is isomorphic to 𝔛, and in that case, 𝔛 is isomorphic to its square, to its hyperplanes, uniformly isomorphic to $𝔛 ⊕ [e_{i}]_{i∈D}$ for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition into uniformly isomorphic copies of itself.

Kategorie tematyczne

• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 168
• Numer: 3
• Strony: 203-216

Daty

wydano

2005

Twórcy

autor

Valentin Ferenczi

• Equipe d'Analyse, Université Paris 6, Couloir 46-0, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France

autor

Christian Rosendal

• Equipe d'Analyse, Université Paris 6, Couloir 46-0, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France
• Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, U.S.A.

Identyfikatory

DOI

10.4064/sm168-3-2