JournalsprimsVol. 43 , No. 3DOI 10.2977/prims/1201012038

On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces

  • Jesús Ferrer

    Universitat de Valencia, Burjassot (Valencia), Spain
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces cover

Abstract

We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak∗-separable admits a closed linear subspace whose dual is not weak∗-separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2-homogeneous polynomials.