Timeline for Subspaces of $L_p([0,1])$ whose unit ball is compact for the topology of convergence in measure
Current License: CC BY-SA 4.0
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| Jan 10, 2022 at 17:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 11, 2021 at 16:25 | answer | added | pietro siorpaes | timeline score: -1 | |
| Jun 16, 2020 at 8:06 | comment | added | user159631 | @DirkWerner This is exactly the kind of result I was looking for. Thank you very much for your help (and for the precise references). | |
| Jun 15, 2020 at 18:57 | comment | added | Dirk Werner | Theorem 4.4 in the paper N. Kalton, DW, ``Property (M), M-ideals, and almost isometric structure of Banach spaces.'' J. Reine Angew. Math. 461, 137-178 (1995) says about a subspace $X\subset L_p[0,1]$, $1<p<\infty$, $p\neq2$, that $X$ embeds almost isometrically into $\ell_p$ if and only if $B_X$ is $L_1$-compact. (This paper is the predecessor of the one you are quoting.) For those spaces, the unit ball is compact in measure. Concerning embeddings into $\ell_p$ see also W.B. Johnson and E. Odell's paper. | |
| Jun 15, 2020 at 14:01 | review | First posts | |||
| Jun 15, 2020 at 14:21 | |||||
| Jun 15, 2020 at 13:58 | history | asked | user159631 | CC BY-SA 4.0 |