Continuity of Extremal Elements in Uniformly Convex Spaces
Complex Variables
2014-10-31 v1
Abstract
In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, we simplify and clarify Ryabykh's proof that for any linear functional on a uniformly convex Bergman space with kernel in a certain Hardy space, the extremal functional belongs to the corresponding Hardy space.
Cite
@article{arxiv.1301.7326,
title = {Continuity of Extremal Elements in Uniformly Convex Spaces},
author = {Timothy Ferguson},
journal= {arXiv preprint arXiv:1301.7326},
year = {2014}
}
Comments
9 pages. Very minor changes from published version