In which Banach spaces is the polar of every convex cone convex

TL;DR

This paper characterizes Banach spaces where the polar of every convex cone remains convex, focusing on those that are uniformly convex and uniformly smooth, using the normalized duality map.

Contribution

It provides a characterization of Banach spaces with convex polar cones based on uniform convexity and smoothness properties.

Findings

Identifies conditions under which convex cones have convex polars

Uses normalized duality map for characterization

Focuses on uniformly convex and smooth Banach spaces

Abstract

Using the notion of the normalized duality map it is characterized the class of the uniformly convex uniformly smooth Banach spaces in which each convex cone has a convex polar.