Generalizations of some classical theorems to D-normal operators on Hilbert spaces

[摘要] We say that a Drazin invertible operator T on Hilbert space is of class $[DN]$ if $T^{D}T^{*} = T^{*}T^{D}$. 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 $(\beta)$. Finally, we generalize a very famous result on products of normal operators due to I. Kaplansky to D-normal matrices.

[学科分类] 电力

[关键词] Drazin inverse;D-normal operator;Fuglede–Putnam theorem;Bishop property