Topological duals of locally convex function spaces

Pennanen, Teemu und Perkkiö, Ari-Pekka (2022): Topological duals of locally convex function spaces. In: Positivity, Bd. 26, Nr. 1

Abstract

This paper studies topological duals of locally convex function spaces that are natural generalizations of Frechet and Banach function spaces. The dual is identified with the direct sum of another function space, a space of purely finitely additive measures and the annihilator of L-infinity. This allows for quick proofs of various classical as well as new duality results e.g. in Lebesgue, Musielak-Orlicz, Orlicz-Lorentz space and spaces associated with convex risk measures. Beyond Banach and Frdchet spaces, we obtain completeness and duality results in general paired spaces of random variables.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik ; Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1385-1292
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892