Skip to Main content Skip to Navigation
Journal articles

Non-linear factorization of linear operators

Abstract : We show, in particular, that a linear operator between finite-dimensional normed spaces, which factors through a third Banach space Z via Lipschitz maps, factors linearly through the identity from L(infinity)([0, 1], Z) to L(1)([0, 1], Z) (and thus, in particular, through each L(p)(Z), for 1 < p < infinity) with the same factorization constant. It follows that, for each 1 < p < infinity, the class of L(p) spaces is closed under uniform (and even coarse) equivalences. The case p = 1 is new and solves a problem raised by Heinrich and Mankiewicz in 1982. The proof is based on a simple local-global linearization idea.
Document type :
Journal articles
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-00693044
Contributor : Admin Lama <>
Submitted on : Tuesday, May 1, 2012 - 7:43:55 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

Links full text

Identifiers

Citation

W. B. Johnson, Bernard Maurey, G. Schechtman. Non-linear factorization of linear operators. Bulletin of the London Mathematical Society, London Mathematical Society, 2009, 41 (?), pp.663--668. ⟨10.1112/blms/bdp040⟩. ⟨hal-00693044⟩

Share

Metrics

Record views

417