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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4707 or http://arXiv.org/abs/0805.4707 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4707 or in gzipped form by using subject line get 0805.4707 to: math@arXiv.org.