Lower bounds for norms of products of polynomials

Benitez, C; Sarantopoulos, Y; Tonge, A

dc.contributor.author	Benitez, C	en
dc.contributor.author	Sarantopoulos, Y	en
dc.contributor.author	Tonge, A	en
dc.date.accessioned	2014-03-01T01:13:53Z
dc.date.available	2014-03-01T01:13:53Z
dc.date.issued	1998	en
dc.identifier.issn	0305-0041	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12764
dc.subject	Lower Bound	en
dc.subject.classification	Mathematics	en
dc.subject.other	SHARP INEQUALITIES	en
dc.subject.other	SPACES	en
dc.title	Lower bounds for norms of products of polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S030500419800259X	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S030500419800259X	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	Let P-1,...,P-n be polynomials in one or several real or complex variables. Several authors, working with a variety of norms, have given estimates for a constant ill depending only on the degrees of P-1,...,P-n such that parallel to P(1)parallel to...parallel to P(n)parallel to less than or equal to M parallel to P-1...P(n)parallel to. In this paper we show that inequalities of this type are valid for polynomials on any complex Banach space. Our method provides optimal constants. We also derive analogous inequalities for polynomials on real Banach spaces, but the constants we obtain are generally not optimal. The search for optimal constants does however lead to an interesting open problem in Hilbert space geometry. When we restrict attention to products of linear functionals, we find new characterizations of complex l(1)(n) (n greater than or equal to 2), real l(1)(2), and real Hilbert space.	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	Mathematical Proceedings of the Cambridge Philosophical Society	en
dc.identifier.doi	10.1017/S030500419800259X	en
dc.identifier.isi	ISI:000077568600002	en
dc.identifier.volume	124	en
dc.identifier.issue	3	en
dc.identifier.spage	395	en
dc.identifier.epage	408	en