From 777f9d3fd8caf56e6bc6999a4b05379307d0733f Mon Sep 17 00:00:00 2001
From: Justin Gassner <justin.gassner@mailbox.org>
Date: Tue, 12 Sep 2023 07:36:33 +0200
Subject: Initial commit

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 pages/tomita-takesaki-theory/index.md              |  9 +++++++++
 pages/tomita-takesaki-theory/standard-subspaces.md | 19 +++++++++++++++++++
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 create mode 100644 pages/tomita-takesaki-theory/index.md
 create mode 100644 pages/tomita-takesaki-theory/standard-subspaces.md

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

diff --git a/pages/tomita-takesaki-theory/index.md b/pages/tomita-takesaki-theory/index.md
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+---
+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
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+---
+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 }}
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