Timeline for Classical subspaces of non-atomic Banach lattices
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24, 2018 at 10:58 | comment | added | Tomasz Kania | For an example illustrating @MikhailOstrovskii 's claim, see mathoverflow.net/questions/171680/… | |
| Feb 24, 2018 at 6:12 | comment | added | Mikhail Ostrovskii | You can try to look at the paper Tokarev, E. V. A symmetric Banach function space that does not contain $\ell_p$ $(1\le p<\infty)$ and $c_0$ (Russian) Funktsional. Anal. i Prilozhen. 18 (1984), no. 2, 75-76 (it was translated into English). I should warn you that this author is known for making errors in proofs. | |
| Feb 23, 2018 at 22:49 | comment | added | user114263 | I only care that it contains the classical spaces as subspaces. I do not require that they be sublattices. | |
| Feb 23, 2018 at 22:28 | comment | added | Jochen Glueck | By the way, two remarks concerning the spaces $c_0$ and $\ell^1$: (i) A Banach lattice $E$ is a KB-space if and only if $E$ does not contain $c_0$ as a closed subspace if and only if $E$ does not contain $c_0$ as a closed sublattice [1, Theorems 2.4.12 and 2.5.6]; (ii) A Banach lattice $E$ is reflexive if and only $E$ does not contain $c_0$ nor $\ell^1$ as a closed subspace if and only if $E$ does not contain $c_0$ nor $\ell^1$ as a closed sublattice [1, Theorem 2.4.15]. Reference: [1] "Peter Meyer-Nieberg: Banach Lattices (1991)" | |
| Feb 23, 2018 at 22:23 | comment | added | Jochen Glueck | Do you wish your non-discrete Banach lattice to contain the classical sequence spaces as closed sublattices, or just as closed subspaces? | |
| Feb 23, 2018 at 20:50 | history | asked | user114263 | CC BY-SA 3.0 |