Within the class of CPD operators, nth roots preserve subnormality, quasinormality, normality, and the 3-isometry property.
Stankovi´ c, Subnormalnth roots of matricially and spherically quasinormal pairs,Filomat 37(2023) 5325-5331
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CPD $n$th roots of subnormal operators are subnormal
Within the class of CPD operators, nth roots preserve subnormality, quasinormality, normality, and the 3-isometry property.