Continuity of Extremal Elements in Uniformly Convex Spaces

Timothy Ferguson

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arXiv · 1301.7326

Continuity of Extremal Elements in Uniformly Convex Spaces

Timothy Ferguson

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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.

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Timothy Ferguson. 2013-01-30. Continuity of Extremal Elements in Uniformly Convex Spaces. https://arxiv.org/abs/1301.7326

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