6533b85dfe1ef96bd12bdc7e
RESEARCH PRODUCT
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces
Jesús Ferrersubject
Discrete mathematicsPure mathematicsPolynomialDifference polynomialsGeneral MathematicsBounded functionHomogeneous polynomialBanach spaceReflexive spaceLinear subspaceMathematicsSeparable spacedescription
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 2homogeneous polynomials.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-01-01 | Publications of the Research Institute for Mathematical Sciences |