  We say that a complex number $\lambda$ is an extended eigenvalueof a bounded
linear operator T on a Hilbert space H if there exists anonzero bounded linear
operator X acting on H, called extended eigen-vector associated to $\lambda$,
and satisfying the equation T X = $\lambda$XT . In thispaper we describe the
sets of extended eigenvalues and extended eigen-vectors for the product of a
positive and a self-adjoint operator whichare both injective. We also treat the
case of normal operators.
