Advanced Search

For two Banach spaces X and Y, we write $di{m}_{\ell }\left(X\right)=di{m}_{\ell }\left(Y\right)$ 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 $di{m}_{\ell }\left(X\right)=di{m}_{\ell }\left(Y\right)$ 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...