A class of Banach spaces with few non-strictly singular operators

Argyros, SA; Lopez-Abad, J; Todorcevic, S

dc.contributor.author	Argyros, SA	en
dc.contributor.author	Lopez-Abad, J	en
dc.contributor.author	Todorcevic, S	en
dc.date.accessioned	2014-03-01T01:21:42Z
dc.date.available	2014-03-01T01:21:42Z
dc.date.issued	2005	en
dc.identifier.issn	0022-1236	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16328
dc.subject	Diagonal operators	en
dc.subject	Hereditarily indecomposable Banach spaces	en
dc.subject	Reflexive Banach spaces	en
dc.subject	Strictly singular operators	en
dc.subject	Transfinite Schauder bases	en
dc.subject	Unconditional basic sequences	en
dc.subject	Uncountable codings	en
dc.subject.classification	Mathematics	en
dc.subject.other	MIXED TSIRELSON SPACES	en
dc.subject.other	SEQUENCE	en
dc.title	A class of Banach spaces with few non-strictly singular operators	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jfa.2004.11.001	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jfa.2004.11.001	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	We construct a family (X-gamma) of reflexive Banach spaces with long (countable as well as uncountable) transfinite bases but with no unconditional basic sequences. The method we introduce to achieve this allows us to considerably control the structure of subspaces of the resulting spaces as well as to precisely describe the corresponding spaces on non-strictly singular operators. For example, for every pair of countable ordinals gamma, beta, we are able to decompose every bounded linear operator from X-gamma to X-beta as the sum of a diagonal operator and an strictly singular operator. We also show that every finite-dimensional subspace of any member X-gamma of our class can be moved by and (4 + epsilon)-isomorphism to essentially any region of any other member X-delta or our class. Finally, we find subspaces X of X-gamma such that the operator space L(X, X-gamma) is quite rich but any bounded operator T from X into X is a strictly singular pertubation of a scalar multiple of the identity. (c) 2004 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Functional Analysis	en
dc.identifier.doi	10.1016/j.jfa.2004.11.001	en
dc.identifier.isi	ISI:000228731500004	en
dc.identifier.volume	222	en
dc.identifier.issue	2	en
dc.identifier.spage	306	en
dc.identifier.epage	384	en