Small subspaces of Lp

• 成果类型: Article
• 署名作者: Haydon, Richard; Odell, Edward; Schlumprecht, Thomas
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.1.5
• 发表日期: 2011
• 页码: 169-209
• 关键词: banach-spaces; complemented subspaces; quotients; index; bases; sums

摘要

We prove that if X is a subspace of L-p (2 < p < infinity), then either X embeds isomorphically into l(p) circle plus l(2) or X contains a subspace Y, which is isomorphic to l(p)(l(2)). We also give an intrinsic characterization of when X embeds into fp e 2 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 L-p 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.