On the interpolation of injective or projective tensor products of Banach spaces
نویسندگان
چکیده
منابع مشابه
On The Interpolation of Injective or Projective Tensor Products of Banach Spaces
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]θ = [E0, E1]θ⊗̂[F0, F1]θ, 0 < θ < 1. We find also conditions on the spaces E0, E1, F0 and F1 , so that the following holds [E0 ∨ ⊗F0, E1 ∨ ⊗F1...
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Let X, Y and Z be Banach spaces, and let ∏ p(Y, Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T : X⊗̂ǫY −→ Z is 1-summing if and only if a naturally associated operator T : X −→ ∏ 1(Y, Z) is 1-summing. This result need not be true if X is not a £∞-space. For p > 1, several examples are given with X = C[0, 1] t...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1991
ISSN: 0022-1236
DOI: 10.1016/0022-1236(91)90072-d