John decompositions: selecting a large part

Details John decompositions: selecting a large part John decompositions: selecting a large part

1999-09-19

arxiv.org/abs/math/9909110v1

Mathematics

Functional Analysis

Scientific paper

We extend the invertibility principle of J. Bourgain and L. Tzafriri to operators acting on arbitrary decompositions id = \sum x_j \otimes x_j, rather than on the coordinate one. The John's decomposition brings this result to the local theory of Banach spaces. As a consequence, we get a new lemma of Dvoretzky-Rogers type, where the contact points of the unit ball with its maximal volume ellipsoid play a crucial role. This is applied to embeddings of l_\infty^k into finite dimensional spaces.

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