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Diniz, D. and MuñozFernández, Gustavo A. and Pellegrino, Daniel and SeoaneSepúlveda, Juan B. (2012) The asymptotic growth of the constants in the BohnenblustHille inequality is optimal. Journal of Functional Analysis, 263 (2). pp. 415428. ISSN 00221236
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Official URL: http://www.sciencedirect.com/science/journal/00221236
URL  URL Type 

http://www.sciencedirect.com  Publisher 
http://arxiv.org/pdf/1108.1550v2.pdf  Organisation 
Abstract
The search of sharp estimates for the constants in the BohnenblustHille inequality, besides its challenging nature, has quite important applications in different fields of mathematics and physics. For homogeneous polynomials, it was recently shown that the BohnenblustHille inequality (for complex scalars) is hypercontractive. This result, interesting by itself, has found direct striking applications in the solution of several important problems. For multilinear mappings, precise information on the asymptotic behavior of the constants of the BohnenblustHille inequality is of particular importance for applications in Quantum Information Theory and multipartite Bell inequalities. In this paper, using elementary tools, we prove a quite surprising result: the asymptotic growth of the constants in the multilinear BohnenblustHille inequality is optimal. Besides its intrinsic mathematical interest and potential applications to different areas, the mathematical importance of this result also lies in the fact that all previous estimates and related results for the last 80 years (such as, for instance, the multilinear version of the famous Grothendieck theorem for absolutely summing operators) always present constants Cm's growing at an exponential rate of certain power of m.
Item Type:  Article 

Uncontrolled Keywords:  BohnenblustHille inequality; Asymptotic growth; Optimal constants; Absolutely summing operators 
Subjects:  Sciences > Mathematics > Functional analysis and Operator theory 
ID Code:  19941 
Deposited On:  13 Feb 2013 16:25 
Last Modified:  28 Nov 2016 09:28 
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