diff options
Diffstat (limited to 'pages/tomita-takesaki-theory')
-rw-r--r-- | pages/tomita-takesaki-theory/index.md | 1 | ||||
-rw-r--r-- | pages/tomita-takesaki-theory/standard-subspaces.md | 17 |
2 files changed, 6 insertions, 12 deletions
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 %} |