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The norm of the product of polynomials in infinite dimensions

Boyd, C.
; 
Ryan, R. A.
Identifiers
http://hdl.handle.net/10379/8893
 https://doi.org/10.13025/24576
Publication Date
2006-02-02
Keywords
polynomials, geometry of banach spaces, norm inequalities, sharp inequalities, variables, mappings, theorem
Type
Article
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Citation
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
Abstract
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.
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Publisher
Cambridge University Press (CUP)
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (1)