A nearly uniformly convex space which is not a -space
Denka Kutzarova (1989)
Acta Universitatis Carolinae. Mathematica et Physica
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Displaying similar documents to “Cyclic pairs and common best proximity points in uniformly convex Banach spaces”
A nearly uniformly convex space which is not a -space
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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. ...
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