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 (Formula presented.), Duggal transform (Formula presented.), and mean transform (Formula presented.). In particular, we show that under the condition that ǀTǀUǀTǀ = ǀTǀ²U where T = UǀTǀ is the polar decomposition, if one of T, (Formula presented.), and (Formula presented.) is subscalar of finite order, then (Formula presented.) 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.