Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces

• Autorzy: P. Holický , O. F. K. Kalenda , L. Veselý , L. Zajíček
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B10: Duality and reflexivity
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: 55
• Numer: 3
• Strony: 211-217

Daty

wydano

2007

Twórcy

autor

P. Holický

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

autor

O. F. K. Kalenda

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

autor

L. Veselý

• Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

autor

L. Zajíček

• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/ba55-3-3