Subspaces with a common complement in a Banach space

Drivaliaris, D; Yannakakis, N

dc.contributor.author	Drivaliaris, D	en
dc.contributor.author	Yannakakis, N	en
dc.date.accessioned	2014-03-01T01:27:20Z
dc.date.available	2014-03-01T01:27:20Z
dc.date.issued	2007	en
dc.identifier.issn	0039-3223	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18403
dc.subject	Algebraic complement	en
dc.subject	Common complement	en
dc.subject	Completely asymptotic subspaces	en
dc.subject	Equivalently positioned subspaces	en
dc.subject	Geometry of Banach spaces	en
dc.subject	Pair of subspaces	en
dc.subject	Relative position	en
dc.subject.classification	Mathematics	en
dc.subject.other	HILBERT-SPACE	en
dc.subject.other	PROJECTIONS	en
dc.subject.other	PERSPECTIVITY	en
dc.subject.other	EQUIVALENCE	en
dc.subject.other	ALGEBRAS	en
dc.subject.other	LATTICE	en
dc.title	Subspaces with a common complement in a Banach space	en
heal.type	journalArticle	en
heal.identifier.primary	10.4064/sm182-2-4	en
heal.identifier.secondary	http://dx.doi.org/10.4064/sm182-2-4	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution S on X exchanging the two subspaces, such that I + S is bounded from below on their union. Moreover, we show that, in a separable Hilbert space, the only pairs of subspaces with a common complement are those which are either equivalently positioned or not completely asymptotic to one another. We also obtain characterizations for the existence of a common complement for subspaces with closed sum. © Instytut Matematyczny PAN, 2007.	en
heal.publisher	POLISH ACAD SCIENCES INST MATHEMATICS	en
heal.journalName	Studia Mathematica	en
dc.identifier.doi	10.4064/sm182-2-4	en
dc.identifier.isi	ISI:000252417400004	en
dc.identifier.volume	182	en
dc.identifier.issue	2	en
dc.identifier.spage	141	en
dc.identifier.epage	164	en