Continuity of extremal elements in uniformly convex spaces

Ferguson, Timothy

doi:10.1090/S0002-9939-09-09892-X

Continuity of extremal elements in uniformly convex spaces
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by Timothy Ferguson PDF

Proc. Amer. Math. Soc. 137 (2009), 2645-2653

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 function belongs to the corresponding Hardy space.

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