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

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

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1487-1491.doi: 10.1016/S0252-9602(16)30084-4

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

曾清平¹, 钟怀杰²

1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350002, China;
2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

收稿日期:2014-10-16 修回日期:2016-03-12 出版日期:2016-10-25 发布日期:2016-10-25
作者简介:Qingping ZENG,zqpping2003@163.com;Huaijie ZHONG,zhonghuaijie@sina.com
基金资助:
This work has been supported by National Natural Science Foundation of China (11301077, 11301078, 11401097, 11501108) and Natural Science Foundation of Fujian Province (2015J01579, 2016J05001).

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

Qingping ZENG¹, Huaijie ZHONG²

1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350002, China;
2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

Received:2014-10-16 Revised:2016-03-12 Online:2016-10-25 Published:2016-10-25
Supported by:
This work has been supported by National Natural Science Foundation of China (11301077, 11301078, 11401097, 11501108) and Natural Science Foundation of Fujian Province (2015J01579, 2016J05001).

摘要/Abstract

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‖^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)^*.

关键词: *-class A operator, *-paranormal operator, Riesz idempotent

Abstract:

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

中图分类号:

47A10

曾清平, 钟怀杰. RIESZ IDEMPOTENT OF (n,k)-QUASI-*-PARANORMAL OPERATORS[J]. 数学物理学报(英文版), 2016, 36(5): 1487-1491.

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

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

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