Let A and B be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.
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 results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.
The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of normal operators are given, without using the known 2πi-congruence-free hypothesis. This is a continuation of a recent work by the second author.
We are mainly concerned with the result of Kaplansky on the composition of two normal operators in the case in which at least one of the operators is unbounded.
The purpose of this work is to give a topological condition for the usual product of two closed operators acting in a Hilbert space to be closed.
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