  The existence of a counterexample to the infinite-dimensional Carleson
embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg.
We provide an explicit construction of such an example. We also obtain a
non-constructive example of particularly simple form; the density function of
the measure (with respect to a certain weighted area measure) is the
tensor-square of a Hilbert space-valued analytic function. This special
structure of the measure has implications for Hankel-like operators appearing
in control theory.
