  Following Grothendieck's characterization of Hilbert spaces we consider
operator spaces $F$ such that both $F$ and $F^*$ completely embed into the dual
of a C*-algebra. Due to Haagerup/Musat's improved version of
Pisier/Shlyakhtenko's Grothendieck inequality for operator spaces, these spaces
are quotients of subspaces of the direct sum $C\oplus R$ of the column and row
spaces (the corresponding class being denoted by $QS(C\oplus R)$). We first
prove a representation theorem for homogeneous $F\in QS(C\oplus R)$ starting
from the fundamental sequences defined by column and row norms of unit vectors.
Under a mild regularity assumption on these sequences we show that they
completely determine the operator space structure of $F$ and find a canonical
representation of this important class of homogeneous Hilbertian operator
spaces in terms of weighted row and column spaces. This canonical
representation allows us to get an explicit formula for the exactness constant
of an $n$-dimensional subspace $F_n$ of $F$ involving the fundamental
sequences. Similarly, we have formulas for the the projection (=injectivity)
constant of $F_n$. They also permit us to determine the completely 1-summing
maps in Effros and Ruan's sense between two homogeneous spaces $E$ and $F$ in
$QS(C\oplus R)$.
