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Diffstat (limited to 'pages/unbounded-operators/graph-and-closedness.md')
| -rw-r--r-- | pages/unbounded-operators/graph-and-closedness.md | 15 |
1 files changed, 5 insertions, 10 deletions
diff --git a/pages/unbounded-operators/graph-and-closedness.md b/pages/unbounded-operators/graph-and-closedness.md index a9bf738..04a6789 100644 --- a/pages/unbounded-operators/graph-and-closedness.md +++ b/pages/unbounded-operators/graph-and-closedness.md @@ -6,17 +6,12 @@ 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. -# spellchecker:dictionaries latex -# spellchecker:words Hellinger Toeplitz innerp hilb Schwarz functionals enspace Riesz --- # {{ page.title }} - -{: .definition-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 $y=Tx$. +{% 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 %} |