If I understood you right:
If we have two-commuting bounded linear operators (if they Hermitian), in quantum physics it's mean, if I'm right, that we can't make such observation and determine the state of both parameters of the system. But the suggestion, that we have such operator that commute to both can possibly make both states — A and B determined simultaneously.
So, for my small opinion, Com(A, B) didn't exist or equal to zero.
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