[Banach] Abstract of a paper by Michael Cwikel and Alon Ivtsan

This is an announcement for the paper "Counterexamples for interpolation of compact Lipschitz operators" by Michael Cwikel and Alon Ivtsan.

Abstract: Let (A_0,A_1) and (B_0,B_1) be Banach couples with A_0 contained in A_1 and B_0 contained in B_1. Let T:A_1 --> B_1 be a possibly nonlinear operator which is a compact Lipschitz map of A_j into B_j for j=0,1. It is known that T maps the Lions-Peetre space (A_0,A_1)_\theta,q boundedly into (B_0,B_1)_\theta,q for each \theta in (0,1) and each q in [1,\infty), and that this map is also compact if if T is linear. We present examples which show that in general the map T:(A_0,A_1)_\theta,q --> (B_0,B_1)_\theta,q is not compact.

Archive classification: math.FA

Mathematics Subject Classification: 46B70 (primary), 47H99, 46B50 (secondary)

Remarks: 22 pages. The main results are on pages 1-8. Later pages contain some additional more elaborate counterexamples

The source file(s), 14cCounterexample.tex: 76306 bytes e1e2yellow.jpg: 50818 bytes enen+1yellowgreen.jpg: 102039 bytes etnew.jpg: 65214 bytes newen-yellow.jpg: 56125 bytes, is(are) stored in gzipped form as 0906.2432.tar.gz with size 250kb. The corresponding postcript file has gzipped size .

Submitted from: mcwikel@math.technion.ac.il

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