Update

1 files changed, 6 insertions, 11 deletions

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 %}