Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666009 | Advances in Mathematics | 2013 | 13 Pages |
Abstract
This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop–Phelps–Bollobás property, i.e., they are approximated by norm attaining Asplund operators at the same time that a point where the approximated operator almost attains its norm is approximated by a point at which the approximating operator attains it. To prove this result we use the weak∗∗-to-norm fragmentability of weak∗∗-compact subsets of the dual of Asplund spaces and we need to observe a Urysohn type result producing peak complex-valued functions in uniform algebras that are small outside a given open set and whose image is inside a Stolz region.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
B. Cascales, A.J. Guirao, V. Kadets,