2021/03/10 by José L. Ansorena, Ansorena, José L., Glenier Bello +1
Mathematics · Social Sciences · #28B05 #46A16 #46A32 #46A40 #46E30 #46G10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Urbanization and City Planning
paper · pdf · doi:10.48550/arxiv.2103.06144
openalex publication_date 2021/03/10 · openalex created_date 2023/03/01 · openalex updated_date 2026/07/28
We present a new approach to define a suitable integral for functions with\nvalues in quasi-Banach spaces. The integrals of Bochner and Riemann have\ndeficiencies in the non-locally convex setting. The study of an integral for\np-Banach spaces initiated by Vogt is neither totally satisfactory, since\nthere are quasi-Banach spaces which are p-convex for all 0<p<1, so it is\nnot always possible to choose an optimal p to develop the integration. Our\nmethod puts the emphasis on the galb of the space, which permits a precise\ndefinition of its convexity. The integration works for all spaces of galbs\nknown in the literature. We finish with a fundamental theorem of calculus for\nour integral.\n