Lineability of non-differentiable Pettis primitives

2014/03/08 by B. Bongiorno, Bongiorno, B., U. B. Darju +3
Mathematics · #28B05 #46G10 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.1403.1908

openalex publication_date 2014/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued Pettis integrable function on [0; 1] whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that ND, the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to ND.

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