Subspaces with a common complement in a Banach space

• Autorzy: Dimosthenis Drivaliaris , Nikos Yannakakis
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 46B20: Geometry and structure of normed linear spaces
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 182
• Numer: 2
• Strony: 141-164

Daty

wydano

2007

Twórcy

autor

Dimosthenis Drivaliaris

• Department of Financial and Management Engineering, University of the Aegean, 31, Fostini St., 82100 Chios, Greece

autor

Nikos Yannakakis

• Department of Mathematics, National Technical University of Athens, Iroon Polytexneiou 9, 15780 Zografou, Greece

Identyfikatory

DOI

10.4064/sm182-2-4