Every infinite dimensional separable Hilbert space H {\displaystyle {\color {Yellow}{\mathfrak {H}}}} owns a non-separable companion Hilbert space H {\displaystyle {\color {Yellow}{\mathcal {H}}}}
The non-separable Hilbert space H {\displaystyle {\color {Yellow}{\mathcal {H}}}} embeds its separablecompanion Hilbert space H {\displaystyle {\color {Yellow}{\mathfrak {H}}}}
Together these Hilbert spaces constitute the base model ᙜ
H ⇛ {\displaystyle {\color {Yellow}{\mathfrak {H}}}{\color {White}\Rrightarrow }} ᙜ ⇚ H {\displaystyle {\color {White}\Lleftarrow }{\color {Yellow}{\mathcal {H}}}}