Timeline for Subspaces of finite codimension in Banach spaces
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2017 at 21:07 | comment | added | Chris Judge | A couple of comments to make the second paragraph more transparent (The author did express some doubt). Let $F'$ denote the span of $\{y_k\}$. Since $\{x_k\}$ is a basis, one finds that $F' \cap F = \{0\}$. For each $x \in E$ we have $x +F = \sum x_i^*(x+F)\cdot x_i$ and hence there exists $f \in F$ so that $x = f + \sum x_i^*(x+F)\cdot y_i$. Thus $E=F+F'$. | |
| Jul 7, 2010 at 20:08 | comment | added | Pietro Majer | to be precise, the question about complementation makes sense for any linear subspace, why. I would rather say: "a complemented linear subspace is necessarily closed". | |
| Jul 7, 2010 at 10:55 | vote | accept | Kestutis Cesnavicius | ||
| Jul 7, 2010 at 10:31 | history | answered | Matthew Daws | CC BY-SA 2.5 |