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Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property
ÅSvald LimaVegard LimaEve Ojasubject
Banach spacesAbsolutely summing operatorsTwo-trunk treesContinuous functions on [01]Linear B-splinesBounded approximation propertiesdescription
AbstractLet X be a Banach space. For describing the space P(C[0,1],X) of absolutely summing operators from C[0,1] to X in terms of the space X itself, we construct a tree space ℓ1tree(X) on X. It consists of special trees in X which we call two-trunk trees. We prove that P(C[0,1],X) is isometrically isomorphic to ℓ1tree(X). As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X∗-valued sequence spaces.
year | journal | country | edition | language |
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Journal of Functional Analysis |