# Hilbert Book Model Project/Slide 3

Every infinite dimensional separable Hilbert space ${\displaystyle {\color {Yellow}{\mathfrak {H}}}}$
owns a non-separable companion Hilbert space ${\displaystyle {\color {Yellow}{\mathcal {H}}}}$
The non-separable Hilbert space ${\displaystyle {\color {Yellow}{\mathcal {H}}}}$ embeds its separable
companion Hilbert space ${\displaystyle {\color {Yellow}{\mathfrak {H}}}}$
${\displaystyle {\color {Yellow}{\mathfrak {H}}}{\color {White}\Rrightarrow }}$ ${\displaystyle {\color {White}\Lleftarrow }{\color {Yellow}{\mathcal {H}}}}$