This is an announcement for the paper "Subspaces with a common complement in a Banach space" by D. Drivaliaris and N. Yannakakis.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20; 46C05; 47A05

Citation: Studia Mathematica 182 (2) (2007), 141-164

The source file(s), common_arxiv.tex: 74237 bytes, is(are) stored in gzipped form as 0805.4707.gz with size 16kb. The corresponding postcript file has gzipped size 104kb.

Submitted from: d.drivaliaris@fme.aegean.gr

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