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Holomorphic and Operator TheoryAdvanced Banach Space TheoryAnalytic and geometric function theory

Space of Besicovitch functions isometric to $\boldsymbol{c}$

J. Bobok, J. Dudák

2026.3.8BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN

DOI: 10.36045/j.bbms.251216

Abstract

We prove that there exists a subspace of $C([0,1])$ isometric to $\boldsymbol{c}$ (the space of convergent sequences) such that every nonzero function in the subspace is Besicovitch, i.e. the function does not have a one-sided derivative (not even infinite) at any point.

Citation format

BOBOK, J.; DUDÁK, J. Space of besicovitch functions isometric to $\boldsymbol{c}$. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2026, 33(1).