On the distance of subspaces of l p n l^ n_ p to l p k l^ k_ p

It is proved that if lpnis well-isomorphic to X Y and X either has small dimension or is a Euclidean space, then Y is well-isomorphic to lpk, k = dim Y. The proofs use new forms of the finite dimensional decomposition method. It is shown that the constant of equivalence between a normalized Kunconditional basic sequence in lpnand a subsequence of the unit vector basis of lpnis greatest, up to a constant depending on K, when the sequence spans a 2-Euclidean space. 1991 American Mathematical Society.

On the distance of subspaces of l p n l^ n_ p to l p k l^ k_ p Academic Article