Spectral Analysis Of Generalized Aluthge Transform For The Bounded Linear Operators

The polar decomposition and generalized Aluthge transform of linear operators are some important research contents of linear operators, they paly a key role in the spectral analysis and descriptions of invariant subspaces for linear operators.For a bounded linear operator T acting on the Hilbert space, the relations of point spectrum, residual spectrum, continuous spectrum, approximate spectrum and spectrum between T and its generalized Aluthge transform△λ(T)=|T|λU|T|1-λ(0<λ<1)are given in this thesis. Moreover, some examples are constructed to illustrate the correctness of the obtained conclusions.