Linear operators for which $T\sp{\ast} T$ and $TT\sp{\ast} $\ commute
Linear operators for which $T\sp{\ast} T$ and $TT\sp{\ast} $\ commute
Linear operators T for which ${T^\ast }T$ and $T{T^\ast }$ commute are studied. Examples are given to show that this class of operators is distinct from several other operator classes. It is proven that if ${T^\ast }T$ and $T{T^\ast }$ commute and T is hyponormal, then T has an invariant …