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| author | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-20 12:01:07 +0100 |
|---|---|---|
| committer | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-20 12:01:07 +0100 |
| commit | 8b9bb9346c217874670b0f1798ab6f1cb28fdb83 (patch) | |
| tree | 167336a47f0d19dc8b0897f4e94be0e44933eeb2 /pages/unbounded-operators | |
| parent | 7c66b227a494748e2a546fb85317accd00aebe53 (diff) | |
| download | site-8b9bb9346c217874670b0f1798ab6f1cb28fdb83.tar.zst | |
Update
Diffstat (limited to 'pages/unbounded-operators')
4 files changed, 3 insertions, 21 deletions
diff --git a/pages/unbounded-operators/adjoint-operators.md b/pages/unbounded-operators/adjoint-operators.md index 96933db..b1c9207 100644 --- a/pages/unbounded-operators/adjoint-operators.md +++ b/pages/unbounded-operators/adjoint-operators.md @@ -1,12 +1,8 @@ --- title: Adjoint Operators parent: Unbounded Operators -nav_order: 1 +nav_order: 3 published: false -description: > - The Hellinger–Toeplitz Theorem states that an everywhere-defined symmetric - operator on a Hilbert space is bounded. We give a proof using the Uniform - Boundedness Theorem. We give another proof using the Closed Graph Theorem. --- # {{ page.title }} diff --git a/pages/unbounded-operators/graph-and-closedness.md b/pages/unbounded-operators/graph-and-closedness.md index 04a6789..73b00a0 100644 --- a/pages/unbounded-operators/graph-and-closedness.md +++ b/pages/unbounded-operators/graph-and-closedness.md @@ -1,11 +1,7 @@ --- title: Graph and Closedness parent: Unbounded Operators -nav_order: 1 -description: > - The Hellinger–Toeplitz Theorem states that an everywhere-defined symmetric - operator on a Hilbert space is bounded. We give a proof using the Uniform - Boundedness Theorem. We give another proof using the Closed Graph Theorem. +nav_order: 2 --- # {{ page.title }} diff --git a/pages/unbounded-operators/hellinger-toeplitz-theorem.md b/pages/unbounded-operators/hellinger-toeplitz-theorem.md index 09046f4..67cdeea 100644 --- a/pages/unbounded-operators/hellinger-toeplitz-theorem.md +++ b/pages/unbounded-operators/hellinger-toeplitz-theorem.md @@ -1,7 +1,7 @@ --- title: Hellinger–Toeplitz Theorem parent: Unbounded Operators -nav_order: 10 +nav_order: 1 description: > The Hellinger–Toeplitz Theorem states that an everywhere-defined symmetric operator on a Hilbert space is bounded. We give a proof using the Uniform diff --git a/pages/unbounded-operators/quadratic-forms.md b/pages/unbounded-operators/quadratic-forms.md index cb1c44a..e2183ff 100644 --- a/pages/unbounded-operators/quadratic-forms.md +++ b/pages/unbounded-operators/quadratic-forms.md @@ -3,16 +3,6 @@ title: Quadratic Forms parent: Unbounded Operators nav_order: 5 published: false -description: > - The Hellinger–Toeplitz Theorem states that an everywhere-defined symmetric - operator on a Hilbert space is bounded. We give a proof using the Uniform - Boundedness Theorem. We give another proof using the Closed Graph Theorem. --- # {{ page.title }} - -{% definition Graph of an Operator %} -The *graph* of an operator $T$ in a Hilbert space $\hilb{H}$ -is the set of all pairs $(x,y) \in \hilb{H}\times\hilb{H}$ -where $x$ lies in the domain of $T$ and $y=Tx$. -{% enddefinition %} |