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Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

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Holický P., Kalenda O., Veselý L., Zajíček L.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 55

nr 3

211-217

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.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Holický P.

1 Kalenda O.

1 Veselý L.

1 Zajíček L.

1 2007

Wyniki wyszukiwania

Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces