6533b857fe1ef96bd12b38ab

RESEARCH PRODUCT

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

Eve OjaÅSvald LimaVegard Lima

subject

Discrete mathematicsSequenceTree (descriptive set theory)Approximation propertyBounded functionInfinite-dimensional vector functionBanach spaceSpace (mathematics)Operator spaceAnalysisMathematics

description

Abstract Let 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 l 1 tree ( 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 l 1 tree ( X ) . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X ∗ -valued sequence spaces.

yearjournalcountryeditionlanguage
2010-12-01Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2010.07.017