JournalsprimsVol. 41 , No. 2DOI 10.2977/prims/1145475359

An Approximate Rolle’s Theorem for Polynomials of Degree Four in a Hilbert Space

  • Jesús Ferrer

    Universitat de Valencia, Burjassot (Valencia), Spain
An Approximate Rolle’s Theorem for Polynomials of Degree Four in a Hilbert Space cover

Abstract

We show that the fourth degree polynomials that satisfy Rolle’s Theorem in the unit ball of a real Hilbert space are dense in the space of polynomials that vanish in the unit sphere. As a consequence, we obtain a sort of approximate Rolle’s Theorem for those polynomials.