2004/01/24 by Omran Kouba · 1 citation
Mathematics · #math.FA #msc:46B70 #msc:47A56 #msc:47A68 #msc:46M05 #msc:46B07
published as J. Funct. Anal. 96 (1991), 38-61 · 26 pages
arxiv created 2004/01/24 · arxiv updated 2009/12/01
We prove a general result on the factorization of matrix-valued analytic functions. We deduce that if (E0,E1) and (F0,F1) are interpolation pairs with dense intersections, then under some conditions on the spaces E0, E1, F0 and F1, we have [E0⊗ F0,E1⊗ F1]t= [E0, E1]t⊗[F0, F1]t, 0 < t< 1. We find also conditions on the spaces E0, E1, F0 and F1, so that the following holds [E0\wcheck⊗ F0,E1\wcheck⊗ F1]t= [E0,E1]t\wcheck⊗ [F0,F1]t, 0 <t< 1. Some applications of these results are also considered.