On classes of banach spaces admitting ""small""; universal spaces

Dodos, P

dc.contributor.author	Dodos, P	en
dc.date.accessioned	2014-03-01T01:31:32Z
dc.date.available	2014-03-01T01:31:32Z
dc.date.issued	2009	en
dc.identifier.issn	0002-9947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19809
dc.subject	L ∞- spaces	en
dc.subject	Non-universal spaces	en
dc.subject	Schauder bases	en
dc.subject	Strongly bounded classes	en
dc.subject.classification	Mathematics	en
dc.subject.other	OPERATORS	en
dc.subject.other	BASES	en
dc.title	On classes of banach spaces admitting ""small""; universal spaces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1090/S0002-9947-09-04913-7	en
heal.identifier.secondary	http://dx.doi.org/10.1090/S0002-9947-09-04913-7	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	We characterize those classes C of separable Banach spaces admitting a separable universal space Y (that is, a space Y containing, up to isomorphism, all members of C) which is not universal for all separable Banach spaces. The characterization is a byproduct of the fact, proved in the paper, that the class NU of non-universal separable Banach spaces is strongly bounded. This settles in the affirmative the main conjecture from Argyros and Dodos (2007). Our approach is based, among others, on a construction of L∞- spaces, due to J. Bourgain and G. Pisier. As a consequence we show that there exists a family {Yξ : ξ < ω1 } of separable, non-universal, L∞-spaces which uniformly exhausts all separable Banach spaces. A number of other natural classes of separable Banach spaces are shown to be strongly bounded as well. © 2009 American Mathematical Society.	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	Transactions of the American Mathematical Society	en
dc.identifier.doi	10.1090/S0002-9947-09-04913-7	en
dc.identifier.isi	ISI:000271831600007	en
dc.identifier.volume	361	en
dc.identifier.issue	12	en
dc.identifier.spage	6407	en
dc.identifier.epage	6428	en