From 28407333ffceca9b99fae721c30e8ae146a863da Mon Sep 17 00:00:00 2001
From: Justin Gassner <justin.gassner@mailbox.org>
Date: Wed, 14 Feb 2024 07:24:38 +0100
Subject: Update

---
 pages/unbounded-operators/hellinger-toeplitz-theorem.md | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

(limited to 'pages/unbounded-operators/hellinger-toeplitz-theorem.md')

diff --git a/pages/unbounded-operators/hellinger-toeplitz-theorem.md b/pages/unbounded-operators/hellinger-toeplitz-theorem.md
index 07d6b81..fea54be 100644
--- a/pages/unbounded-operators/hellinger-toeplitz-theorem.md
+++ b/pages/unbounded-operators/hellinger-toeplitz-theorem.md
@@ -6,7 +6,6 @@ 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.
-# cspell:words Hellinger Toeplitz Schwarz Riesz functionals
 ---
 
 # {{ page.title }}
@@ -25,10 +24,9 @@ $$
 \innerp{Tx}{y} = \innerp{x}{Ty} \quad \forall x,y \in D(T).
 $$
 
-{: .theorem-title }
-> Hellinger–Toeplitz theorem
->
-> An everywhere-defined symmetric operator on a Hilbert space is bounded.
+{% theorem * Hellinger–Toeplitz Theorem %}
+An everywhere-defined symmetric operator on a Hilbert space is bounded.
+{% endtheorem %}
 
 Consequently, a symmetric Hilbert space operator
 that is (truly) unbounded
@@ -75,7 +73,6 @@ Divide by $\norm{Tx_n}$ (if nonzero)
 to obtain $\norm{Tx_n} \le \norm{f_n}$ for all but finitely many $n$.
 Thus $(\norm{Tx_n})$ is a bounded sequence,
 contradicting $\norm{Tx_n} \to \infty$.
-{{ site.qed }}
 
 ---
 
@@ -113,4 +110,3 @@ $$
 A sequence of complex numbers has at most one limit,
 hence $\innerp{Tx}{y} = \innerp{z}{y}$ for all $y$.
 By the Riesz representation theorem, $Tx=z$.
-{{ site.qed }}
-- 
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