Commutators Which Commute with One Factor
نویسندگان
چکیده
Let A and B be n × n matrices, let C = ABA−1B−1 be the multiplicative commutator of A and B, and assume AC = CA. Olga Taussky (1961) examined the structure of A and B for the case where A and B are unitary. Marcus and Thompson (1966) generalized her results to the case where A and C are assumed normal. We look at this problem for general A, with particular attention to the cases where A is diagonalizable or nonderogatory. Now let [A,B] = AB − BA be the additive commutator of A and B and assume A commutes with [A,B]. The finitedimensional version of a theorem of Putnam tells us that if A is normal, then A and B commute. We show that the same conclusion holds when A is diagonalizable. If A is nonderogatory, then A and B can be simultaneously triangularized.
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