Exponentials of Normal Operators and Commutativity of Operators: A New Approach

We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some similarities results by Berberian and Embry as well as the celebrated Fuglede theorem.Comment: 05 page

On the triviality of domains of powers and adjoints of closed operators

The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators