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On C*-algebras which cannot be decomposed into tensor products with both factors infinite-dimensional
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math.OAmath.FA
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algebrascannotclassdecomposedinfinite-dimensionalresulttensorbanach
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We prove that C*-algebras which, as Banach spaces, are Grothendieck cannot be decomposed into a tensor product of two infinite-dimensional C*-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*-algebras.
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