JEDNOSTKA NAUKOWA KATEGORII A+

Cantor–Bernstein theorems for Orlicz sequence spaces

Tom 102 / 2014

Carlos E. Finol, Marcos J. González, Marek Wójtowicz Banach Center Publications 102 (2014), 71-88 MSC: Primary 46B03, 46A45; Secondary 46B25, 46B45. DOI: 10.4064/bc102-0-4

Streszczenie

For two Banach spaces $X$ and $Y$, we write $\dim _\ell(X)= \dim _\ell(Y)$ if $X$ embeds into $Y$ and vice versa; then we say that \emph{$X$ 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 $\mathcal F$ has the Cantor–Bernstein property if for every $X,Y\in {\cal F}$ the condition $\dim _\ell(X)= \dim _\ell(Y)$ 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.

Autorzy

  • Carlos E. FinolEscuela de Matemáticas
    Universidad Central de Venezuela
    P.O.Box 48059
    Caracas 1041-A, Venezuela
    e-mail
  • Marcos J. GonzálezDepartamento de Matemáticas
    Universidad Simón Bolívar
    Apartado 89000
    Caracas 1080-A, Venezuela
    e-mail
  • Marek WójtowiczInstytut Matematyki
    Uniwersytet Kazimierza Wielkiego
    Pl. Weyssenhoffa 11
    85-072 Bydgoszcz, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek