Zeros of Polynomials on Banach Spaces: The Real Story

Zeros of Polynomials on Banach Spaces: The Real Story Let E be a real Banach space. We show that either E admits a positive definite 2-homogeneous polynomial or every 2-homogeneous polynomial on E has an infinite dimensional subspace on which it is identically zero. Under addition assumptions, we show that such subspaces are non-separable. We examine analogous results for nuclear and absolutely (1,2)-summing 2-homogeneous polynomials and give necessary and sufficient conditions on a compact set K so that C(K) admits a positive definite 2-homogeneous polynomial or a positive definite nuclear 2-homogeneous polynomial. Positivity Springer Journals

Zeros of Polynomials on Banach Spaces: The Real Story

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Kluwer Academic Publishers
Copyright © 2003 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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  • Zeros of Real Polynomials
    Aron, R.M.; Gonzalo, R.; Zagorodnyuk, A.

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