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Results in Mathematics

, 74:24 | Cite as

Some Results on the Classes of D-normal Operators and n-power D-normal Operators

  • M. DanaEmail author
  • R. Yousefi
Article

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.

Keywords

Drazin inverse Fuglede–Putnam theorem D-normal operators n-power D-normal operators 

Mathematics Subject Classification

47B15 47B20 15A09 

Notes

Acknowledgements

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of KurdistanSanandajIslamic Republic of Iran

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