We consider the C^*-numerical range and numerical radius for adjointable operators acting on Hilbert C^*-modules over C^*-algebras. This C^*-numerical range is a subset of the underlying C^*-algebra and coincides with the classical numerical range in the framework of Hilbert space. We obtain several properties of the C^*-numerical range and numerical radius, including the inequality between the spectral radius and the numerical radius, leading us to prove that the underlying operator norm and the numerical radius are equivalent norms.

Hilbert C^*-module, adjointable operator, numerical range, numerical radius.