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Good 2 -subspaces of L p , p>2. (English) Zbl 1194.46014
In a recent preprint, R. Haydon, E. Odell and Th. Schlumprecht [“Small subspaces of L p ,” arXiv:0711.3919] show that a Hilbertian subspace of L p , p>2, contains a further subspace Z that is (1+ε)-isomorphic to 2 and complemented in L p by a projection of norm (1+ε)γ p , where γ p is the L p -norm of a standard Gaussian random variable. Their proof uses random measures and types à la Krivine and Maurey. Here, the author gives another proof that avoids these means and depends only on a version of the central limit theorem for martingales.
MSC:
46B09Probabilistic methods in Banach space theory
46B25Classical Banach spaces in the general theory of normed spaces
46E30Spaces of measurable functions