Square roots of semihyponormal operators have scalar extensions. (Q1408359)

A Hilbert space operator \(T\in B(H)\) is semi-hyponormal if \(|T^*|\leq |T|\). The author continues his study of the classes of Hilbert space operators which are subscalar. Here, the author proves that if \(T\) is the square root of a semi-hyponormal operator (i.e., \(T\in B(H)\) is such that \(T^2\) is semi-hyponormal), then \(T\) is subscalar of order \(4\). Applications, mostly routine, are considered.