The norm of the product of polynomials in infinite dimensions
Ryan, R. A.
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Boyd, C. Ryan, R. A. (2006). The norm of the product of polynomials in infinite dimensions. Proceedings of the Edinburgh Mathematical Society 49 , 17-28
Given a Banach space E and positive integers k and l we investigate the smallest constant C that satisfies parallel to P parallel to parallel to Q parallel to <= C parallel to PQ parallel to for all k-homogeneous polynomials P and l-homogeneous polynomials Q on E. Our estimates are obtained using multilinear maps, the principle of local reflexivity and ideas from the geometry of Banach spaces (type and uniform convexity). We also examine the analogous problem for general polynomials on Banach spaces.