Using boundaries to find smooth norms

Abstract

The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with $C^k$ smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of $B_{X^{\ast }}$, namely boundaries. Of interest is that the main result unifies two quite well known results. In the final section, some new corollaries are given.

14 pages

References in corpus (2)

• Polyhedrality in Pieces
• Smooth norms and approximation in Banach spaces of the type C(K)

Cited by in corpus (5)

• Smooth and polyhedral approximation in Banach spaces
• Smooth and polyhedral norms via fundamental biorthogonal systems
• Approximation of norms on Banach spaces
• Some remarks on smooth renormings of Banach spaces
• Topology, isomorphic smoothness and polyhedrality in Banach spaces