Majorization in de Branges spaces II. Banach spaces generated by majorants

TL;DR

This paper explores Banach spaces created by majorants within de Branges spaces, analyzing their structure and properties, revealing that they are often nonreflexive and nonseparable, thus deepening understanding of their geometric and functional characteristics.

Contribution

It introduces and studies Banach spaces generated by admissible majorants in de Branges spaces, highlighting their geometric and topological properties, especially nonreflexivity and nonseparability.

Findings

Banach spaces generated by majorants are generally nonreflexive.

These spaces are typically nonseparable.

The study reveals their complex interplay with de Branges space structure.

Abstract

This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by admissible majorants. We study their interplay with the original de Branges space structure, and their geometry. In particular, we will show that, generically, they will be nonreflexive and nonseparable.