Abstract
Every Banach space is isomorphic to a space with the property that the norm-attaining operators are dense in the space of all operators into it, for any given domain space. A super-reflexive space is arbitrarily nearly isometric to a space with this property.
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References
E. Bishop and R. R. Phelps,A proof that every Banach space is subreflexive, Bull. Am. Math. Soc.67 (1961), 97–98.
J. Bourgain,On dentability and the Bishop-Phelps property, Isr. J. Math.28 (1977), 265–271.
M. M. Day,Normed Linear Spaces, 3rd ed., Springer, 1972.
J. Diestel and J. J. Uhl, Jr.,Vector Measures, American Mathematical Society Mathematical Surveys No. 15 (1977).
J. Johnson and J. Wolfe,Norm attaining operators, Studia Math.65 (1979), 7–19.
J. Lindenstrauss,On operators which attain their norm, Isr. J. Math.1 (1963), 139–148.
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Partington, J.R. Norm attaining operators. Israel J. Math. 43, 273–276 (1982). https://doi.org/10.1007/BF02761947
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DOI: https://doi.org/10.1007/BF02761947