New Results on Some Transforms of Operators in Hilbert Spaces

Abstract

In this paper, we explore various transforms associated with a bounded linear operator T on a Hilbert space. These transforms include the Aluthge, \(\lambda \)-Aluthge, Duggal, generalized mean, and \(\lambda \)-mean transforms. Our aim is to investigate the connections between T and these transforms, focusing on aspects such as norm inequalities and numerical ranges, while also highlighting certain essential properties. Furthermore, we aim to determine the conditions under which an operator T coincides in norm with its transformed counterparts through these transformations. Several characterizations and properties are also derived.