Subspaces with a common complement in a Banach space
| dc.creator | Drivaliaris, D. | |
| dc.creator | Yannakakis, N. | |
| dc.date | 2008-05-30 | |
| dc.date.accessioned | 2026-07-07T09:41:52Z | |
| dc.date.available | 2026-07-07T09:41:52Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0805.4707 | |
| dc.identifier | http://arxiv.org/abs/0805.4707 | |
| dc.identifier | Studia Mathematica 182 (2) (2007), 141-164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161979 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B20; 46C05; 47A05 | |
| dc.title | Subspaces with a common complement in a Banach space | |
| dc.type | text |