Spline Characterizations of the Radon-Nikod\'{y}m property
Markus Passenbrunner
TL;DR
This paper characterizes the Radon-Nikodým property of Banach spaces using polynomial spline sequences, providing a new analytical framework for understanding this property.
Contribution
It introduces necessary and sufficient conditions for Banach spaces to have the Radon-Nikodým property based on spline sequence characterizations.
Findings
Provides a spline-based criterion for the Radon-Nikodým property.
Establishes equivalence between spline sequence conditions and the property.
Advances understanding of Banach space geometry through spline analysis.
Abstract
We give necessary and sufficient conditions for a Banach space having the Radon-Nikod\'{y}m property in terms of polynomial spline sequences.
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