Premium
Complemented Subspaces of Spaces Obtained by Interpolation
Author(s) -
Garling D. J. H.,
MontgomerySmith S. J.
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-44.3.503
Subject(s) - banach space , mathematics , separable space , interpolation space , linear subspace , pure mathematics , subspace topology , banach manifold , approximation property , martingale (probability theory) , interpolation (computer graphics) , quotient space (topology) , quotient , lp space , discrete mathematics , mathematical analysis , functional analysis , computer science , animation , biochemistry , chemistry , computer graphics (images) , gene
If Z is a quotient of a subspace of a separable Banach space X , and V is any separable Banach space, then there is a Banach couple ( A 0 , A 1 ) such that A 0 and A 1 are isometric to X ⊕ V , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z . Thus many properties of Banach spaces, including having non‐trivial cotype, having the Radon–Nikodym property, and having the analytic unconditional martingale difference sequence property, do not pass to intermediate spaces.