On The Interpolation of Injective or Projective Tensor Products of Banach Spaces

Details On The Interpolation of Injective or Projective Tensor Products of Banach Spaces On The Interpolation of Injective or Projective Tensor Products of Banach Spaces

2004-01-24

arxiv.org/abs/math/0401337v1

J. Funct. Anal. 96 (1991), 38-61

Mathematics

Functional Analysis

26 pages

Scientific paper

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

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