(Asymptotic) uniform smoothness, ball separation and residuality results
Pradipta Bandyopadhyay, Deepak Gothwal
TL;DR
This paper explores the properties of asymptotically uniformly smooth norms, providing a characterization, and demonstrates that the set of such norms is residual, with related results for other smoothness and intersection properties.
Contribution
It introduces a new ball separation characterization for AUS norms and proves the residuality of the set of equivalent AUS norms, extending to related smoothness properties.
Findings
AUS norms can be characterized via ball separation.
The set of equivalent AUS norms is residual.
Similar residuality results hold for uniformly smooth norms and UMIP.
Abstract
In this article, we discuss a ball separation characterisation of asymptotically uniformly smooth (AUS) norms. We use this characterisation to prove the residuality of the set of equivalent AUS norms. We discuss similar residuality results for uniformly smooth norms and norms with uniform Mazur intersection property (UMIP).
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques