Classes of strictly singular operators and their products

Androulakis, G; Dodos, P; Sirotkin, G; Troitsky, VG

dc.contributor.author	Androulakis, G	en
dc.contributor.author	Dodos, P	en
dc.contributor.author	Sirotkin, G	en
dc.contributor.author	Troitsky, VG	en
dc.date.accessioned	2014-03-01T01:29:59Z
dc.date.available	2014-03-01T01:29:59Z
dc.date.issued	2009	en
dc.identifier.issn	0021-2172	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19431
dc.subject	banach space	en
dc.subject.classification	Mathematics	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	SUBSPACE THEOREM	en
dc.title	Classes of strictly singular operators and their products	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11856-009-0010-4	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11856-009-0010-4	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	V. D. Milman proved in [20] that the product of two strictly singular operators on L p [0, 1] (1 ≤ p < ∞) mpact. In this note we utilize Schreier families xi in order to define the class of Sξ -strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this class are compact, under the assumption that the underlying Banach space has finitely many equivalence classes of Schreier-spreading sequences. Finally we define the class of ξ -hereditarily indecomposable Banach spaces and we examine the operators on them. © 2008 Hebrew University Magnes Press.	en
heal.publisher	HEBREW UNIV MAGNES PRESS	en
heal.journalName	Israel Journal of Mathematics	en
dc.identifier.doi	10.1007/s11856-009-0010-4	en
dc.identifier.isi	ISI:000261261300010	en
dc.identifier.volume	169	en
dc.identifier.issue	1	en
dc.identifier.spage	221	en
dc.identifier.epage	250	en