[Banach] Abstract of a paper by B. Bongiorno, U. B. Darju, and L. Di Piazza

This is an announcement for the paper "Lineability of non-differentiable Pettis primitives" by B. Bongiorno, U. B. Darju, and L. Di Piazza.

Abstract: Let X be an in?nite-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 di?erentiable. Using their technique and some new ideas we show that ND, the set of strongly measurable Pettis integrable functions with nowhere weakly di?erentiable primitives, is lineable, i.e., there is an in?nite dimensional vector space whose nonzero vectors belong to ND.

Archive classification: math.FA

Mathematics Subject Classification: 46G10, 28B05

Submitted from: ubdarj01@louisville.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1403.1908

or

http://arXiv.org/abs/1403.1908