2009/06/12 by Michael Ćwikel, Michael Cwikel, Cwikel, Michael +2
Mathematics · #46B50 (secondary) #46B70 (primary) #47H99 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #math.FA #msc:46B50 #msc:46B70 #msc:47H99
paper · pdf · doi:10.48550/arxiv.0906.2432
22 pages. The main results are on pages 1-8. Later pages contain some additional more elaborate counterexamples
arxiv created 2009/06/12 · openalex publication_date 2009/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (A0,A1) and (B0,B1) be Banach couples with A0 contained in A1 and B0 contained in B1. Let T:A1 --> B1 be a possibly nonlinear operator which is a compact Lipschitz map of Aj into Bj for j=0,1. It is known that T maps the Lions-Peetre space (A0,A1)θ,q boundedly into (B0,B1)θ,q for each θin (0,1) and each q in [1,∞), and that this map is also compact if if T is linear. We present examples which show that in general the map T:(A0,A1)θ,q --> (B0,B1)θ,q is not compact.