Dual Kadec Klee property and fixed points

作者：Saint Raymond Jean^*

来源：Journal of Functional Analysis, 2017, 272(9): 3825-3844.

DOI：10.1016/j.jfa.2016.12.016

• Convex functions
• Banach spaces
• Dual Kadec-Klee property
• Fixed points

A Banach space X is said to have the dual Kadec-Klee property BEE on the unit sphere of the dual space X* the weak*-topology coincides with the norm-topology. A. AminiHarandi and M. Fakhar extended a theorem of B. Ricceri concerning the Kadec-Klee property by showing that if X has the dual Kadec-Klee property then for every comfit mapping P Bx(*) -> X\ {0} there exists some f in the unit sphere of X* such that (f, (f)) = parallel to(f)parallel to and conjectured that this yields a necessary and sufficient condition for X to have the dual Kadec-Klee property. We prove here that it is almost the case: we introduce a weakening of the dual KadecKlee property, here called the NAKK* property, and show that this property is equivalent.to the above property about compact mappings from Bx(*) to X \ {0}.

• 出版日期2017-5-1