On a separable, infinite dimensional Banach space X, a bounded linear operator T : X → X is said to be hypercyclic on X if there is a vector x ∈ X whose orbit orb (T, x) = {x, Tx, T x, T x, . . .} is dense in X. Such a vector x is called a hypercyclic vector for T . When the operator T : X → X is hypercyclic on X and its adjoint operator T ∗ : X∗ → X∗ is hypercyclic on the dual space X∗ of X, then we say that T is dual hypercyclic. Since an orbit is a countable set, dual hypercyclicity can only take place when both X and X∗ are separable. However, X is separable whenever its dual X∗ is, but the converse is not always true. Separability does not present an issue when the Banach space X is indeed a Hilbert space H, because the adjoint T ∗ is a bounded linear operator on H itself. In fact, it was the Hilbert space setting that the concept of dual hypercyclicity started to develop. A fundamental question is whether dual hypercyclic operators on H can ever exist. This question was originally raised by Herrero [4]. The first example of such an operator was found by Salas [6]. Later he [7] provided another example using a general result for hypercyclic bilateral weighted shift operators. Recently generalizations of dual hypercyclic operators to a Banach space X were studied. For instance, Petersson [5] showed that any infinite dimensional Banach space X with a shrinking symmetric basis, such as c0 and p with 1 < p < ∞, admits a dual hypercyclic operator T : X → X. Then Salas [8] showed that any Banach space X with a separable dual spaceX∗ admits a dual hypercyclic operator. More recently, Shkarin [10] studied dual hypercyclic tuples of operators on Banach spaces, and Salas [9] studied dual disjoint hypercyclic operators. In the present paper we return to the setting of a separable, infinite dimensional Hilbert space H and study compressions of dual hypercyclic operators T : H → H, making use of unique Hilbert space properties. Our main result is Theorem 2 below, which states that the compression of a dual hypercyclic operator T onto a closed subspace M of infinite codimension in H can coincide with any prescribed operator A on M . In other words, if P : H → H is the orthogonal projection onto a closed subspace M with dim (H/M) = ∞, then for any bounded linear