A characterization of \(k\)-hyponormality via weak subnormality. (Q1874616)

In this paper, the authors investigate the relation between \(k\)-hyponormal operators and weakly subnormal operators. The main results are as follows. Firstly, every 2-hyponormal operator is weakly subnormal. Secondly, an operator \(T\) is \((k+1)\)-hyponormal if and only if \(T\) is weakly subnormal and the minimal partially normal extension of \(T\) is \(k\)-hyponormal. As an application, they also present a matricial representation of the minimal normal extension of a subnormal operator as a block staircase matrix.