A note on uniformly dominated sets of summing operators

J. M. Delgado and C. Piñeiro

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 29, 1-6

Abstract:

Let Y be a Banach space that has no finite cotype and p a real number satisfying 1 ≤ p < ∞ . We prove that a set ℳ ⊂ Π p ( X , Y ) is uniformly dominated if and only if there exists a constant C > 0 such that, for every finite set { ( x i , T i ) : i = 1 , … , n } ⊂ X × ℳ , there is an operator T ∈ Π p ( X , Y ) satisfying π p ( T ) ≤ C and ‖ T i x i ‖ ≤ ‖ T x i ‖ for i = 1 , … , n .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:616897

DOI: 10.1155/S0161171202007688

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