Extremal Homogeneous Polynomials on Real Normed Spaces

Kirwan, P; Sarantopoulos, Y; Tonge, AM

dc.contributor.author	Kirwan, P	en
dc.contributor.author	Sarantopoulos, Y	en
dc.contributor.author	Tonge, AM	en
dc.date.accessioned	2014-03-01T01:14:40Z
dc.date.available	2014-03-01T01:14:40Z
dc.date.issued	1999	en
dc.identifier.issn	0021-9045	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13172
dc.subject	normed space	en
dc.subject.classification	Mathematics	en
dc.title	Extremal Homogeneous Polynomials on Real Normed Spaces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jath.1996.3273	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jath.1996.3273	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	If P is a continuous nz-homogeneous polynomial on a real normed space and P is the associated symmetric m-linear form, the ratio \\P\\/\\P\\ always lies between 1 and m(m)/m!. We show that, as in the complex case investigated by Sarantopoulos (1987, Proc. Amer. Math. Sec. 99, 340-346), there are P's for which \\P\\/\\P\\= m(m)/m! and for which ??P achieves norm if and only if the normed space contains an isometric copy of l(1)(m). However, unlike the complex case, we find a plentiful supply of such polynomials provided m greater than or equal to 4. (C) 1999 Academic Press.	en
heal.publisher	ACADEMIC PRESS INC	en
heal.journalName	Journal of Approximation Theory	en
dc.identifier.doi	10.1006/jath.1996.3273	en
dc.identifier.isi	ISI:000079587200001	en
dc.identifier.volume	97	en
dc.identifier.issue	2	en
dc.identifier.spage	201	en
dc.identifier.epage	213	en