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Continuity of extremal elements in uniformly convex spaces
Author(s):
Timothy
Ferguson
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2645-2653.
MSC (2000):
Primary 30H05;
Secondary 46B99
Posted:
March 17, 2009
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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 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
DOI:
10.1090/S0002-9939-09-09892-X
PII:
S 0002-9939(09)09892-X
Received by editor(s):
September 9, 2008
Posted:
March 17, 2009
Communicated by:
Mario Bonk
Copyright of article:
Copyright
2009,
Timothy Ferguson
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