Operators between subspaces and quotients of L1

Abstract : We provide an unified approach of results of L. Dor on the complementation of the range, and of D. Alspach on the nearness from isometries, of small into isomorphisms of L1. We introduce the notion of small subspace of L1 and show lifting theorems for operators between quotients of L1 by small subspaces. We construct a subspace of L1 which shows that extension of isometries from subspaces of L1 to the whole space are no longer true for isomorphisms, and that nearly isometric isomorphisms from subspaces of L1 into L1 need not be near from any isometry.
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Article dans une revue
Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2000, 49 (1), pp.245-286
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https://hal-univ-artois.archives-ouvertes.fr/hal-00441551
Contributeur : Daniel Li <>
Soumis le : mercredi 16 décembre 2009 - 14:40:04
Dernière modification le : jeudi 11 janvier 2018 - 06:12:14

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Gilles Godefroy, Nigel Kalton, Daniel Li. Operators between subspaces and quotients of L1. Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2000, 49 (1), pp.245-286. 〈hal-00441551〉

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