Schatten p-Norm related to some Transforms of Operators

Abstract

This paper explores the p-Schatten norm and various operator transforms, including the λ-Aluthge, Duggal, generalized mean, and λ-mean transforms. The study investigates the relationship between these transforms and an operator T in terms of the p-Schatten norm. Furthermore, it examines the conditions under which an operator T is equal to its transformed counterparts in the p-Schatten norm. The paper also presents several characterizationsand properties relevant to these topics. Lastly, it discusses Schatten norms andequality conditions specifically for the case of p = 1.