×

zbMATH — the first resource for mathematics

Rolle’s theorem fails in \(\ell_ 2\). (English) Zbl 0888.46017
M. Furi and M. Martelli suggested multidimensional analogs of the Rolle theorem [Am. Math. Monthly 102, No. 3, 243-249 (1995; Zbl 0856.26009)]. The author shows by example that these analogs fail in Hilbert space.

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
46B45 Banach sequence spaces
26B05 Continuity and differentiation questions
PDF BibTeX XML Cite
Full Text: DOI