Posinormality, Coposinormality, and Supraposinormality for Some Triangular Operators - Rhaly Jr., H. C. (Sarajevo Journal of Mathematics, 2024)
The range inclusion criterion for posinormality is studied in order to classify more examples of lower triangular factorable matrices as posinormal operators or not. Also, coposinormality is shown to be a hereditary property for lower triangular operators on `l^2, and this leads to some results involving the posispectrum. Finally, sufficient conditions are given for lower triangular factorable matrices to be supraposinormal, and an example is given of a lower triangular factorable matrix that is supraposinormal but neither posinormal nor coposinormal. The last two sections also contain more general results that apply to operators on abstract Hilbert spaces.