Virtual element approximation of eigenvalue problems: Is the stabilization of the right hand side necessary?

The VEM approximation of eigenvalue problems usually involves the appropriate tuning of stabilization parameters, unless self-stabilizing or stabilization-free VEM are used. In this paper we prove that for elliptic self-adjoint eigenvalue problems the stabilization of the mass matrix is not necessary when lower order standard VEM spaces ( k = 1 , 2 ) are adopted. Numerical evidence shows that also for higher order schemes the same result is true on various mesh sequences.