A characterization of Hilbert $C^*$-modules over finite dimensional   $C^*$-algebras
  We show that the unit ball of a full Hilbert $C^*$-module is sequentially compact in a certain weak topology if and only if the underlying $C^*$-algebra is finite dimensional. This provides an answer to the question posed in J. Chmieli\'nski et al [Perturbation of the Wigner equation in inner product $C^*$-modules, J. Math. Phys. 49 (2008), no. 3, 033519; arXiv:0801.2726]. 
Lj. Arambasic, D. Bakic and M. S. Moslehian