Publication: Where do homogeneous polynomials on ln1 attain their norm?
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Publication Date
2004-03-01
Authors
Villanueva, Ignacio
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Publisher
Elsevier
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Abstract
Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ℓ1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ℓ1n. Next we prove that, when n grows, almost every polynomial attains its norm in a face of ‘low’ dimension.