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Author Drivaliaris, D. ♦ Yannakakis, N.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-05-30
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Functional Analysis ♦ 46B20 ♦ 46C05 ♦ 47A05 ♦ math
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.
Description Reference: Studia Mathematica 182 (2) (2007), 141-164
Educational Use Research
Learning Resource Type Article


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