Topological duals of locally convex function spaces

Pennanen, Teemu and Perkkiö, Ari-Pekka (2022): Topological duals of locally convex function spaces. In: Positivity, Vol. 26, No. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics; Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1385-1292
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892