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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
References
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Additional Information
  • Timothy Ferguson
  • Affiliation: Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, Michigan 48109-1043
  • Email: tjferg@umich.edu
  • Received by editor(s): September 9, 2008
  • Published electronically: March 17, 2009
  • Communicated by: Mario Bonk
  • © Copyright 2009 Timothy Ferguson
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2645-2653
  • MSC (2000): Primary 30H05; Secondary 46B99
  • DOI: https://doi.org/10.1090/S0002-9939-09-09892-X
  • MathSciNet review: 2497477