Authors: | Lopez-Abad, Jorge Todorčević, Stevo |
Title: | A c0-saturated banach space with no long unconditional basic sequences | Journal: | Transactions of the American Mathematical Society | Volume: | 361 | Issue: | 9 | First page: | 4541 | Last page: | 4560 | Issue Date: | 1-Sep-2009 | Rank: | M21 | ISSN: | 0002-9947 | DOI: | 10.1090/S0002-9947-09-04858-2 | Abstract: | We present a Banach space X with a Schauder basis of length ω1 which is saturatedby copies of c0 and such that for every closed decomposition of a closedsubspace X = X0⊕ X1, either X0 or X1 has to be separable. This can be considered as the non-separable counterpart of the notion of hereditarily indecomposable space. Indeed, the subspaces of X have "few operators" in the sense that every bounded operator T: R → X from a subspace X of X into X is the sum of a multiple of the inclusion and a ω1- singular operator, i.e., an operator S which is not an isomorphism on any non-separable subspace of X. We also show that while X is not distortable (being c0-saturated), it is arbitrarily ω1-distortable in the sense that for every λ > 1 there is an equivalent norm |||. ||| on X such that for every non-separable subspace X of X there exist x, y ∈ SX suchthat |||x|||/|||y||| ≥ λ. |
Publisher: | American Mathematical Society |
Show full item record
SCOPUSTM
Citations
4
checked on Sep 16, 2024
Page view(s)
8
checked on Sep 16, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.