Timeline for Every complemented subspace of a $C(T)$-space is an $\mathcal{L}_{\infty}$-space
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2021 at 16:19 | comment | added | Bill Johnson | Yes; that is right. | |
| Apr 22, 2021 at 14:01 | comment | added | Dongyang Chen | In you answer, norm to $1+\epsilon$ the finite dimensional $M$ by finitely many linear functionals of norm one may means that there exists $x^{*}_{1},\cdots,x^{*}_{n}$ of norm one in $X^{*}$ so that $\max_{k}|\langle x^{*}_{k},m\rangle\|\geq \frac{1}{1+\epsilon}\|m\|$ for $m\in M$. Is that right? | |
| Apr 21, 2021 at 15:29 | vote | accept | Dongyang Chen | ||
| Apr 21, 2021 at 15:28 | comment | added | Dongyang Chen | As for Question 2, J. Lindenstrauss and H. P. Rosenthal pointed out that it follows from the proof of Theorem 2.1 and James's distortion theorem that if $X$ is $C$-complemented in $C(K)$ , then $X$ is an $\mathcal{L}_{\infty, 9C+\epsilon}$ space for every $\epsilon>0$. | |
| Apr 21, 2021 at 15:23 | comment | added | Dongyang Chen | Question 1 comes from the proof of Theorem 2.1 in J. Lindenstrauss and H. P. Rosenthal's paper in 1969. You do not misunderstand my question and you are right. But I have to check your answer. | |
| Apr 21, 2021 at 13:40 | history | answered | Bill Johnson | CC BY-SA 4.0 |