RIESZ IDEMPOTENT OF (n, k)-QUASI-*-PARANORMAL OPERATORS

【摘要】 A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T¹⁺ⁿ（T^kx） ║^1/（1+n）║ T^kx║^n/（1+n）≥║ T*（T^kx）║ 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_λ 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_λ= ker（T- λ） = ker（T- λ）*.更多还原

【Abstract】 A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T¹⁺ⁿ（T^kx） ║^1/（1+n）║ T^kx║^n/（1+n）≥║ T*（T^kx）║ 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_λ 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_λ= ker（T- λ） = ker（T- λ）*.更多还原