Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772248 | Journal of Functional Analysis | 2017 | 20 Pages |
Abstract
A Banach space X is said to have the dual Kadec-Klee property iff on the unit sphere of the dual space Xâ the weak*-topology coincides with the norm-topology. A. Amini-Harandi 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 compact mapping Ï:BXââXâ{0} there exists some f in the unit sphere of Xâ such that ãf,Ï(f)ã=âÏ(f)â 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 Kadec-Klee property, here called the NAKK* property, and show that this property is equivalent to the above property about compact mappings from BXâ to Xâ{0}.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jean Saint Raymond,