Plank problems, polarization and chebyshev constants

Revesz, SGy; Sarantopoulos, Y

dc.contributor.author	Revesz, SGy	en
dc.contributor.author	Sarantopoulos, Y	en
dc.date.accessioned	2014-03-01T01:21:14Z
dc.date.available	2014-03-01T01:21:14Z
dc.date.issued	2004	en
dc.identifier.issn	0304-9914	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16150
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-7544231907&partnerID=40&md5=c42cb829339012fe347ba2c21a4aa000	en
dc.subject	Banach-Mazur distance	en
dc.subject	Characterization of Banach spaces	en
dc.subject	Complexification of Banach spaces	en
dc.subject	Homogeneous polynomials over normed spaces	en
dc.subject	Linear polarization constants	en
dc.subject	Local theory of Banach spaces	en
dc.subject	Plank problem	en
dc.subject	Quasi-monotonous sequences	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	POLYNOMIALS	en
dc.subject.other	PERMANENTS	en
dc.subject.other	SPACES	en
dc.subject.other	PRODUCTS	en
dc.subject.other	NORMS	en
dc.title	Plank problems, polarization and chebyshev constants	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical L-p(mu) spaces. In the case I less than or equal to p less than or equal to 2 we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.	en
heal.publisher	KOREAN MATHEMATICAL SOCIETY	en
heal.journalName	Journal of the Korean Mathematical Society	en
dc.identifier.isi	ISI:000187944900012	en
dc.identifier.volume	41	en
dc.identifier.issue	1	en
dc.identifier.spage	157	en
dc.identifier.epage	174	en