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- W3030372110 abstract "Abstract We say that a Drazin invertible operator T on Hilbert space is of class $[DN]$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>[</mml:mo><mml:mi>D</mml:mi><mml:mi>N</mml:mi><mml:mo>]</mml:mo></mml:math> if $T^{D}T^{*} = T^{*}T^{D}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mi>T</mml:mi><mml:mi>D</mml:mi></mml:msup><mml:msup><mml:mi>T</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:msup><mml:mi>T</mml:mi><mml:mi>D</mml:mi></mml:msup></mml:math> . The authors in (Oper. Matrices 12(2):465–487, 2018) studied several properties of this class. We prove the Fuglede–Putnam commutativity theorem for D-normal operators. Also, we show that T has the Bishop property $(beta)$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>(</mml:mo><mml:mi>β</mml:mi><mml:mo>)</mml:mo></mml:math> . Finally, we generalize a very famous result on products of normal operators due to I. Kaplansky to D-normal matrices." @default.
- W3030372110 created "2020-06-05" @default.
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- W3030372110 date "2020-04-15" @default.
- W3030372110 modified "2023-10-16" @default.
- W3030372110 title "Generalizations of some classical theorems to D-normal operators on Hilbert spaces" @default.
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- W3030372110 doi "https://doi.org/10.1186/s13660-020-02367-z" @default.
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