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We prove that C  $^{\ast }$  -algebras which, as Banach spaces, are Grothendieck cannot be decomposed into a tensor product of two infinite-dimensional C  $^{\ast }$  -algebras. By a result of Pfitzner, this class contains all von Neumann algebras and their norm-quotients. We thus complement a recent result of Ghasemi who established a similar conclusion for the class of SAW  $^{\ast }$  -algebras.

ON C*-ALGEBRAS WHICH CANNOT BE DECOMPOSED INTO TENSOR PRODUCTS WITH BOTH FACTORS INFINITE-DIMENSIONAL