We give a condition on commutativity of a pair of normal operators with respect to the continuous functional calculus. We show a generalization of the theorem of Fuglede and Putnum with respect to the continuous functional calculus.
The article provided here was updated with corrections on 30 March 2017.
"Commuting pairs of normal operators." Nihonkai Math. J. 26 (2) 85 - 90, 2015.