Timeline for Is X+X finitely representable in X?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2016 at 19:15 | comment | added | Mikhail Ostrovskii | This weaker conjecture is true because each finite-dimensional subspace of $X\oplus \ell_2$ is close to being a subspace of $F\oplus \ell_2^n$ for some finite-dimensional subspace $F$ of $X$ and some $n\in\mathbb{N}$. Then you have to use the Dvoretzky theorem and a kind of the Mazur's argument (See Lindenstrauss-Tzafriri, v. I, Lemma 1.a.6) to show that $F\oplus \ell_2^n$ admits a linear embedding into $X$ with distortion bounded by an absolute constant. | |
| Nov 19, 2016 at 19:07 | comment | added | Anso | Thanks! Let me ask you the following weaker conjecture: For any Banach space $X$, $X\oplus \ell_2$ is c.f.r. in $X$. | |
| Nov 19, 2016 at 18:59 | history | edited | Tomasz Kania | CC BY-SA 3.0 |
added 78 characters in body
|
| Nov 19, 2016 at 16:32 | history | answered | Mikhail Ostrovskii | CC BY-SA 3.0 |