Complemented subspaces of spaces obtained by interpolation
D. J. H. Garling, Stephen J. Montgomery-Smith
Abstract
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 (A0,A1) such that A0 and A1 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.
Create a lesson
Related papers
Banach lattices and phase retrieval: A case study for the use of AI in mathematics
Jaume de Dios Pont, Lukas Liehr, David Muñoz-Lahoz et al.
The Banach lattice Lean library
David Muñoz-Lahoz
Equivalent quasi-norms on rearrangement-invariant quasi-Banach function spaces
L. R. Ya. Doktorski
Noncommutative maximal differential transforms associated to averaging operators
Shaohong Liang, Yu Wang, Bang Xu et al.
Boundary Rigidity and Classification of Spectral Transformations Preserving Frame Generators of Normal Diagonal Operator Orbits
Jian Wu
Birkhoff-Orthogonal Takahashi-von Neumann-Jordan Type Constants in Banach Spaces
Junxiang Qi, Zhouping Yin, Qi Liu