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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. Chmielinski et al [Perturbation of the Wigner equation in inner product C*-modules, J. Math. Phys. 49 (2008), no. 3, 033519].

Hilbert C*-module ; finite dimensional C*-algebra ; C*-algebra of compact operators

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