, Volume 33, Issue 2, pp 155-171

Projections onto Hilbertian subspaces of Banach spaces

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In this paper we obtain new estimates for the relative projection constants of subspaces of a Banach spaceY in terms of geometrical properties ofY. Our method gives thatK-convex spaces are locally π-Euclidean. We also get a version of Maurey’s extension theorem for spaces of typep<2.