Cantor-Bernstein theorems for Orlicz sequence spaces

• Autorzy: Carlos E. Finol , Marcos J. González , Marek Wójtowicz
• Języki publikacji: EN

Abstrakty

EN

For two Banach spaces X and Y, we write $dim_{ℓ}(X) = dim_{ℓ}(Y)$ if X embeds into Y and vice versa; then we say that {X and Y have the same linear dimension}. In this paper, we consider classes of Banach spaces with symmetric bases. We say that such a class ℱ has the Cantor-Bernstein property if for every X,Y ∈ ℱ the condition $dim_{ℓ}(X) = dim_{ℓ}(Y)$ implies the respective bases (of X and Y) are equivalent, and hence the spaces X and Y are isomorphic. We prove (Theorems 3.1, 3.3, 3.5) that the class of Orlicz sequence spaces generated by regularly varying Orlicz functions is of this type. This complements some results in this direction obtained earlier by S. Banach (Proposition 1.1), L. Drewnowski (Proposition 1.2), and M. J. Gonzalez, B. Sari and M. Wójtowicz (Theorem 1.4). Our theorems apply to large families of concrete Orlicz spaces.

Kategorie tematyczne

• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 46B45: Banach sequence spaces
• 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: Banach Center Publications
• Rocznik: 2014
• Tom: 102
• Numer: 1
• Strony: 71-88

Daty

wydano

2014

Twórcy

autor

Carlos E. Finol

• Escuela de Matemáticas, Universidad Central de Venezuela, P.O.Box 48059, Caracas 1041-A, Venezuela

autor

Marcos J. González

• Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 89000, Caracas 1080-A, Venezuela

autor

Marek Wójtowicz

• Instytut Matematyki, Uniwersytet Kazimierza Wielkiego, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

Identyfikatory

DOI

10.4064/bc102-0-4