A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has...A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.展开更多
基金supported by National Natural Science Foundation of China(11301077,11301078,11401097,11501108)Natural Science Foundation of Fujian Province(2015J01579,2016J05001)
文摘A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.
