On ℒ_p,λ spaces for small λ

Dale Edward Alspach

Vol. 125 (1986), No. 2, 257–287

DOI: 10.2140/pjm.1986.125.257

Abstract

It is shown for 1 ≤ p≠2 < ∞ that for each ℒ_p,λ subspace X of L_p[0,1] with λ sufficiently close to 1 there is a nonlinear projection from L_p onto X which factors through a linear projection on L₁[0,1] with norm close to 1. Some additional results on representation of certain operators on L₁ are also proved.

Mathematical Subject Classification 2000

Primary: 46E30

Secondary: 46B25

Milestones

Received: 21 May 1985

Published: 1 December 1986