  A Banach space $X$ has the $2$-summing property if the norm of every linear
operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the
operator. Up to a point, the theory of spaces which have this property is
independent of the scalar field: the property is self-dual and any space with
the property is a finite dimensional space of maximal distance to the Hilbert
space of the same dimension. In the case of real scalars only the real line and
real $\ell_\infty^2$ have the $2$-summing property. In the complex case there
are more examples; e.g., all subspaces of complex $\ell_\infty^3$ and their
duals.
