The Drazin Inverse of Generalized-Aluthge Transform
Nan Liu · Journal of Air Force Engineering University · 2014
Let Hbe an infinite Hilbert space and T a bounded linear operator in H,and T~λ and T~λ(*)indicate respectively the generalized Aluthge transform and generalized*-Aluthge transform of T,where λ∈(0,1).By utilizing the method of operational partitioning,the Drazin inverse and Moore-Penrose inverse of T~λ and T~λ(*)are studied.The result proves that for any complex numberμ:①T~λ-μis Drazin invertible if and only if T~λ(*)-μremains;②T~λ-μis Moore-Penrose invertible if and only if T~λ(*)-μremains.Simultaneously,a drawing of the relationships between these two operators,i.e.Drazin inverse and Moore-Penrose inverse,is given.