p-Summing operators on injective tensor products of spaces
نویسندگان
چکیده
منابع مشابه
p-Summing Operators on Injective Tensor Products of Spaces
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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We consider the operator T = m k=1 A 1k ⊗ A 2k (1 ≤ m < ∞), where A lk are n l × n l matrices (k = 1,. .. , m; l = 1, 2), ⊗ means the tensor product. Norm estimates for the resolvent of that operator are derived. By these estimates, we obtain bounds for a solution X of the equation m k=1 A 1k X A 2k = C and explore perturbations of that equation. The norm estimates for the resolvent of T enable...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
سال: 1992
ISSN: 0308-2105,1473-7124
DOI: 10.1017/s0308210500032145