Abstract
Let \({\mathcal {B}}({\mathcal {H}})\) be space of all bounded linear operators on a finite complex Hilbert space \({\mathcal {H}}\), and \(S, T \in {\mathcal {B}}({\mathcal {H}})\). In this paper we investigate a necessary and sufficient condition for the D-normality of ST and TS. Also, we deduce a result relating the factors in a polar decomposition of S to the D-normality of ST and TS. Moreover, we generalize Fuglede–Putnam commutativity theorem for D-normal operators. Finally, we generalize these results when the n-power D-normal operators are considered.
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The authors would like to thank the referees for their valuable comments and suggestions, which allowed improving considerably the writing of the paper.
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Dana, M., Yousefi, R. Some Results on the Classes of D-normal Operators and n-power D-normal Operators. Results Math 74, 24 (2019). https://doi.org/10.1007/s00025-018-0949-8
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DOI: https://doi.org/10.1007/s00025-018-0949-8