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/tomita-takesaki-theory/index.md              |  1 -
 pages/tomita-takesaki-theory/standard-subspaces.md | 17 ++++++-----------
 2 files changed, 6 insertions(+), 12 deletions(-)

(limited to 'pages/tomita-takesaki-theory')

diff --git a/pages/tomita-takesaki-theory/index.md b/pages/tomita-takesaki-theory/index.md
index dd2a312..28b73e6 100644
--- a/pages/tomita-takesaki-theory/index.md
+++ b/pages/tomita-takesaki-theory/index.md
@@ -3,7 +3,6 @@ title: Tomita Takesaki Theory
 nav_order: 10
 has_children: true
 published: false
-# cspell:words
 ---
 
 # {{ page.title }}
diff --git a/pages/tomita-takesaki-theory/standard-subspaces.md b/pages/tomita-takesaki-theory/standard-subspaces.md
index 970c51a..85135aa 100644
--- a/pages/tomita-takesaki-theory/standard-subspaces.md
+++ b/pages/tomita-takesaki-theory/standard-subspaces.md
@@ -2,18 +2,13 @@
 title: Standard Subspaces
 parent: Tomita Takesaki Theory
 nav_order: 1
-# cspell:words
 ---
 
 # {{ page.title }}
 
-{: .definition-title }
-> Definition (Cyclic, Separating, Standard Subspace)
->
-> A closed real linear subspace $H$ of a complex Hilbert space $\hilb{H}$ is called
-> * *cyclic*, if $H+iH$ is dense in $\hilb{H}$,
-> * *separating*, if $H \cap iH = \braces{0}$, and
-> * *standard*, if $H$ is cyclic and separating.
-
-**Proof:**
-{{ site.qed }}
+{% definition Cyclic, Separating, Standard Subspace %}
+A closed real linear subspace $H$ of a complex Hilbert space $\hilb{H}$ is called
+* *cyclic*, if $H+iH$ is dense in $\hilb{H}$,
+* *separating*, if $H \cap iH = \braces{0}$, and
+* *standard*, if $H$ is cyclic and separating.
+{% enddefinition %}
-- 
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