The real plank problem and some applications

Munoz-Fernandez, GA; Sarantopoulos, Y; Seoane-Sepulveda, JB

dc.contributor.author	Munoz-Fernandez, GA	en
dc.contributor.author	Sarantopoulos, Y	en
dc.contributor.author	Seoane-Sepulveda, JB	en
dc.date.accessioned	2014-03-01T01:34:46Z
dc.date.available	2014-03-01T01:34:46Z
dc.date.issued	2010	en
dc.identifier.issn	0002-9939	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20851
dc.subject	Plank problems	en
dc.subject	Polarization constants	en
dc.subject	Product of linear functionals	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	POLARIZATION CONSTANTS	en
dc.subject.other	CHEBYSHEV CONSTANTS	en
dc.subject.other	LINEAR FUNCTIONALS	en
dc.subject.other	HILBERT-SPACES	en
dc.subject.other	LOWER BOUNDS	en
dc.subject.other	POLYNOMIALS	en
dc.subject.other	PRODUCTS	en
dc.subject.other	PERMANENTS	en
dc.subject.other	NORMS	en
dc.title	The real plank problem and some applications	en
heal.type	journalArticle	en
heal.identifier.primary	10.1090/S0002-9939-10-10295-0	en
heal.identifier.secondary	http://dx.doi.org/10.1090/S0002-9939-10-10295-0	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	K. Ball has proved the "complex plank problem": if (x(k))(k=1)(n) is a sequence of norm I vectors in a complex Hilbert space (H, (., .)), then there exists a unit vector x for which \|< x,x(k)>\| >= 1/root n, k = 1,...,n. In general, this result is not true on real Hilbert spaces. However, in special cases we prove that the same result holds true. In general, for some unit vector x we have derived the estimate \|< x,x(k)>\| >= max{root lambda(1)/n, 1/root lambda(n)n}, where lambda(1) is the smallest and lambda(n) is the largest eigenvalue of the Hermitian matrix A = [(x(j), x(k))], j, k = 1,...,n. We have also improved known estimates for the norms of homogeneous polynomials which are products of linear forms on real Hilbert spaces.	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	Proceedings of the American Mathematical Society	en
dc.identifier.doi	10.1090/S0002-9939-10-10295-0	en
dc.identifier.isi	ISI:000278512900029	en
dc.identifier.volume	138	en
dc.identifier.issue	7	en
dc.identifier.spage	2521	en
dc.identifier.epage	2535	en