Interated Aluthge Transforms: a Review

Exploring relations and spectral pictures in Aluthge transforms

Abstract

The Aluthge transform (defined below) of an operator Ton Hilbertspace has been studied extensively, most often in connection with p-hyponormaloperators. In the present paper authors initiated a study of various relationsbetween an arbitrary operator T and its associated, and this study wascontinued in, in which relations between the spectral pictures of T and wereobtained.