This is an announcement for the paper "On the interpolation of injective or projective tensor products of Banach spaces" by Omran Kouba.
Abstract: We prove a general result on the factorization of matrix-valued analytic functions. We deduce that if $(E_0,E_1)$ and $(F_0,F_1)$ are interpolation pairs with dense intersections, then under some conditions on the spaces $E_0$, $E_1$, $F_0$ and $F_1$, we have $$ [E_0\hat\otimes F_0,E_1\hat\otimes F_1]_t= [E_0 ,E_1]_t\hat\otimes[F_0 ,F_1]_t, 0 < t< 1.$$ We find also conditions on the spaces $E_0$, $E_1$, $F_0$ and $F_1$, so that the following holds $$ [E_0\wcheck\otimes F_0,E_1\wcheck\otimes F_1]_t= [E_0,E_1]_t\wcheck\otimes [F_0,F_1]_t, 0 <t< 1.$$ Some applications of these results are also considered.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B70;47A56;47A68;46M05;46B07
Citation: J. Funct. Anal. 96 (1991), 38-61
Remarks: 26 pages
The source file(s), ART3.Tex: 75244 bytes, is(are) stored in gzipped form as 0401337.gz with size 22kb. The corresponding postcript file has gzipped size 93kb.
Submitted from: omran_kouba@hiast.edu.sy
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