Subspaces of c_0 and Lipschitz isomorphisms
We show that the class of subspaces of c_0 is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz isomorphic to c_0 is linearly isomorphic to c_0.
math.FA↗
arXiv subjects
G. Godefroy
Publications and source records attributed to G. Godefroy.
Szlenk indices and uniform homeomorphisms
We prove some rather precise renorming theorems for Banach spaces with Szlenk index $ω_0$. We use these theorems to show the invariance of certain quantitative Szlenk-type indices under uniform homeomorphisms.
math.FA↗
Operators between subspaces and quotients of L1
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.
math.FA↗