Timeline for Complementability of finite dimensional subspaces
Current License: CC BY-SA 4.0
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| Sep 3, 2019 at 20:16 | comment | added | Bill Johnson | It is a nice elementary exercise to prove this is true if $X$ is an $L_p$ space, $1\le p < \infty$. I think I will assign this problem to the students in my functional analysis class. No partial credit for doing the $p=2$ case. | |
| Sep 3, 2019 at 7:37 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 3, 2019 at 5:00 | comment | added | Mikhail Ostrovskii | This is not true because, if we use this condition repeatedly, we would get that there exist subspaces in $X$ with arbitrarily large dimension which are $1+\epsilon$-complemented. This is known to be false in a very strong sense, see G. Pisier, Acta Math. 151 (1983), no. 3-4, 181–208; or his book "Factorization of Linear Operators", 1986, Chapter 10, Corollary 10.8. Pisier mentions that (in 1986) it was unknown whether such spaces can be reflexive, and I do not know whether this question was solved. | |
| Sep 3, 2019 at 3:43 | history | edited | Markus | CC BY-SA 4.0 |
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| Sep 3, 2019 at 1:08 | history | asked | Markus | CC BY-SA 4.0 |