Higher rank numerical ranges of normal operators and unitary dilations

Here we give a closure free description of the higher rank numerical range normal operator acting on separable Hilbert space. This generalizes result Avendaño for self-adjoint operators. It has several interesting applications. We show using Durszt's example that there exists contraction T which intersection ranges all unitary dilations contains as proper subset. strengthen and generalize Wu by providing necessary sufficient condition being equal to possible it. also above is general contraction.