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

doi:10.1016/S0252-9602(16)30084-4

Abstract

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‖^1/(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)-quasi-*-paranormal operator T is self-adjoint and satisfies ranE_λ=ker(T-λ)=ker(T-λ)^*.

Key words: *-class A operator, *-paranormal operator, Riesz idempotent

CLC Number:

47A10

Qingping ZENG, Huaijie ZHONG. RIESZ IDEMPOTENT OF (n,k)-QUASI-*-PARANORMAL OPERATORS[J].Acta mathematica scientia,Series B, 2016, 36(5): 1487-1491.

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