A Bishop–Phelps–Bollobás type theorem for uniform algebras

By B. Cascales, A. Guirao, V. Kadets. 2013

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Abstract This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop–Phelps–Bollobas 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f4ce91bf89ae99f4f98cbe34fbb6fdd6761e3355

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