Subscalarity of operator transforms

In this paper, we provide various connections between a bounded linear operator T and some of its transforms, namely the Aluthge transform , Duggal transform , and mean transform . In particular, we show that under the condition that where is the polar decomposition, if one of T, , and is subscalar of finite order, then is also subscalar of finite order. As an application, we find subscalar operator matrices. We also give several spectral relations. Finally, we provide an equivalent condition under which a weighted shift has a hyponormal iterated mean transform.