Compact perturbations of isometries on separable Hilbert spaces are quasinormal precisely when certain operator conditions hold, with explicit classification for rank-one perturbations of shifts.
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On Quasinormality of compact perturbations of the isometries
Compact perturbations of isometries on separable Hilbert spaces are quasinormal precisely when certain operator conditions hold, with explicit classification for rank-one perturbations of shifts.