Aluthge transformation and *- Aluthge transformation on M class Ak*operator

Abstract

Research works on Operators in Complex Hilbert spaces has been the interest of budding researchers in the recent years. In 1996, Furuta et al studiedAluthge transformation on p-hyponormal operators. Later, in 2001 yamazaki et al studiedAluthge transformation and powers of operators for class A(k)operator. This work was further carried over by Pannayappan et al and D.Senthilkumar et al. In this school work, we studied Aluthge transformation and *- Aluthge transformation for the new class of operator named M class A_k^* operator on a non-zero Complex Hilbert space.