New Results on Some Transforms of Operators in Hilbert Spaces

Abstract

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