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.
Cite this article
Jesús Ferrer, On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces. Publ. Res. Inst. Math. Sci. 43 (2007), no. 3, pp. 685–697DOI 10.2977/PRIMS/1201012038