Norm attaining polynomials

Pappas, A; Sarantopoulos, Y; Tonge, A

dc.contributor.author	Pappas, A	en
dc.contributor.author	Sarantopoulos, Y	en
dc.contributor.author	Tonge, A	en
dc.date.accessioned	2014-03-01T01:26:44Z
dc.date.available	2014-03-01T01:26:44Z
dc.date.issued	2007	en
dc.identifier.issn	0024-6093	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18209
dc.subject.classification	Mathematics	en
dc.subject.other	SPACES	en
dc.title	Norm attaining polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1112/blms/bdl033	en
heal.identifier.secondary	http://dx.doi.org/10.1112/blms/bdl033	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	If L 0 0 is a continuous symmetric n-linear form on a Banach space and (L) over cap is the associated continuous n-homogeneous polynomial, the ratio parallel to L parallel to//parallel to(L) over bar parallel to always lies between 1 and n(n)/n!. At one extreme, if L is defined on Hilbert space, then parallel to L parallel to/parallel to(L) over bar parallel to = 1. If L attains norm on Hilbert space, then L also attains norm; in this case, we give an explicit construction to provide a unit vector x(0) with parallel to(L) over bar parallel to = vertical bar(L) over bar (x(0))vertical bar = parallel to L parallel to. At the other extreme, if parallel to L parallel to/parallel to(L) over bar parallel to = n(n)/n! and L attains norm, then (L) over cap attains norm. We prove that in general the converse is not true.	en
heal.publisher	LONDON MATH SOC	en
heal.journalName	Bulletin of the London Mathematical Society	en
dc.identifier.doi	10.1112/blms/bdl033	en
dc.identifier.isi	ISI:000247052300013	en
dc.identifier.volume	39	en
dc.identifier.issue	2	en
dc.identifier.spage	255	en
dc.identifier.epage	264	en