Banach spaces with a unique nontrivial decomposition

Argyros, SA; Raikoftsalis, T

dc.contributor.author	Argyros, SA	en
dc.contributor.author	Raikoftsalis, T	en
dc.date.accessioned	2014-03-01T01:28:00Z
dc.date.available	2014-03-01T01:28:00Z
dc.date.issued	2008	en
dc.identifier.issn	0002-9939	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18661
dc.subject	prime banach space	en
dc.subject	primary banach space	en
dc.subject	Schauder decomposition	en
dc.subject	hereditarily indecomposable banach space	en
dc.subject	strictly singular operators	en
dc.subject	complemented subspaces	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.title	Banach spaces with a unique nontrivial decomposition	en
heal.type	journalArticle	en
heal.identifier.primary	10.1090/S0002-9939-08-09368-4	en
heal.identifier.secondary	http://dx.doi.org/10.1090/S0002-9939-08-09368-4	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	Motivated by a problem of P. Koszmider we introduce the class of quasi-prime Banach spaces. This class lies between the classes of prime and primary Banach spaces. It is shown that for every 1 <p < ∞ there exists a strictly quasi-prime separable reflexive Banach space ℓp such that ℓp is a complemented subspace of ℓp. A similar result also holds for the case of ℓ1 and C0. More generally, for every separable decomposable prime Banach space Y not containing ℓ1 there exists a strictly quasi-prime Y containing Y as a complemented subspace. We also investigate the operators acting on these spaces as well as the complemented subspaces of their finite powers. © 2008 American Mathematical Society.	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	Proceedings of the American Mathematical Society	en
dc.identifier.doi	10.1090/S0002-9939-08-09368-4	en
dc.identifier.isi	ISI:000256948700028	en
dc.identifier.volume	136	en
dc.identifier.issue	10	en
dc.identifier.spage	3611	en
dc.identifier.epage	3620	en