  We provide conditions ensuring that the KKT-type conditions characterizes the
global optimality for
  quadratically constrained (possibly nonconvex) quadratic programming QCQP
problems in Hilbert spaces. The key property is the convexity of a image-type
set related to the functions appearing in the formulation of the problem.
  The proof of the main result relies on a generalized version of the
(Jakubovich) S-Lemma in Hilbert spaces.
  As an application, we consider the class of QCQP problems with a special form
of the quadratic terms of the constraints.
