Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
hilbert_space [2013/08/31 21:24] nikolaj |
hilbert_space [2013/09/13 19:32] nikolaj |
||
|---|---|---|---|
| Line 3: | Line 3: | ||
| | @#88DDEE: $V$ | | | @#88DDEE: $V$ | | ||
| - | | @#FFBB00: $\mathrm{Hilbert}(V)$ | | + | | @#FFBB00: $\mathcal V \in \mathrm{Hilbert}(V)$ | |
| - | | @#88DDEE: $\mathrm{Hilbert}(V)\subseteq \mathrm{PreHilbert}(V)$ | | + | | @#88DDEE: $\mathcal V \in \mathrm{PreHilbert}(V)$ | |
| - | | $\mathcal V\in \mathrm{Hilbert}(V)$ | | ||
| - | | $v_\infty \in \mathcal V $ | | ||
| | $v\in \mathrm{CauchySeq}(V)$ | | | $v\in \mathrm{CauchySeq}(V)$ | | ||
| + | | @#DDDDDD: $v_\infty \in \mathcal V $ | | ||
| The space $\mathcal V$ is complete: For each Cauchy sequence $(v)_{i\in\mathbb N}$, there is a limit $v_\infty\in\mathcal V$ w.r.t. the natural norm: | The space $\mathcal V$ is complete: For each Cauchy sequence $(v)_{i\in\mathbb N}$, there is a limit $v_\infty\in\mathcal V$ w.r.t. the natural norm: | ||
| Line 18: | Line 17: | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Hilbert_space|Hilbert space]] | Wikipedia: [[http://en.wikipedia.org/wiki/Hilbert_space|Hilbert space]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Pre-Hilbert space]] | [[Pre-Hilbert space]] | ||
| === Requirements === | === Requirements === | ||
| [[Cauchy sequence]] | [[Cauchy sequence]] | ||
