Small subspaces of $L_p$ Academic Article uri icon

abstract

  • We prove that if X is a subspace of Lp (2 < p < ∞), then either X embeds isomorphically into ℓp ⊕ ℓ2 or X contains a subspace Y, which is isomorphic to ℓp(ℓ.2). We also give an intrinsic characterization of when X embeds into ℓp © ℓ2 in terms of weakly null trees in X or, equivalently, in terms of the "infinite asymptotic game" played in X. This solves problems concerning small subspaces of Lp originating in the 1970's. The techniques used were developed over several decades, the most recent being that of weakly null trees developed in the 2000's.

author list (cited authors)

  • Haydon, R., Odell, E., & Schlumprecht, T.

citation count

  • 8

publication date

  • January 2011