6533b82cfe1ef96bd128fb89

RESEARCH PRODUCT

Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property

ÅSvald LimaVegard LimaEve Oja

subject

Banach spacesAbsolutely summing operatorsTwo-trunk treesContinuous functions on [01]Linear B-splinesBounded approximation properties

description

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.

10.1016/j.jfa.2010.07.017http://dx.doi.org/10.1016/j.jfa.2010.07.017