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Diffstat (limited to 'pages/tomita-takesaki-theory/standard-subspaces.md')
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diff --git a/pages/tomita-takesaki-theory/standard-subspaces.md b/pages/tomita-takesaki-theory/standard-subspaces.md new file mode 100644 index 0000000..970c51a --- /dev/null +++ b/pages/tomita-takesaki-theory/standard-subspaces.md @@ -0,0 +1,19 @@ +--- +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 }} |