k-拟-*-A(ｎ)算子的性质

数学季刊 ›› 2012, Vol. 27 ›› Issue (3): 375-381.

k-拟-*-A(ｎ)算子的性质

1. College of Mathematics and Information Science, Henan Normal University 2. Department of Mathematics, Xinxiang University

收稿日期:2010-11-11 出版日期:2012-09-30 发布日期:2023-03-23
作者简介:ZUO Fei(1978-), male, native of Dengzhou, Henan, a lecturer of Henan Normal University, engages in operator theory.
基金资助:
Supported by the Natural Science Foundation of the Department of Education of Henan Province(12B110025,102300410012)

The Properties of k-quasi-∗-A(n) Operator

1. College of Mathematics and Information Science, Henan Normal University 2. Department of Mathematics, Xinxiang University

Received:2010-11-11 Online:2012-09-30 Published:2023-03-23
About author:ZUO Fei(1978-), male, native of Dengzhou, Henan, a lecturer of Henan Normal University, engages in operator theory.
Supported by:
Supported by the Natural Science Foundation of the Department of Education of Henan Province(12B110025,102300410012)

摘要/Abstract

摘要： An operator T is called k-quasi-*-A(n) operator, if T^*k|T¹⁺ⁿ|^2/(1+n)T^k≥T^*k|T^*|²T^k, k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

关键词: k-quasi-?-A(n) operator, quasisimilarity, single valued extension property; Weyl spectrum, essential approximate point spectrum

Abstract: An operator T is called k-quasi-*-A(n) operator, if T^*k|T¹⁺ⁿ|^2/(1+n)T^k≥T^*k|T^*|²T^k, k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

Key words: k-quasi-?-A(n) operator, quasisimilarity, single valued extension property; Weyl spectrum, essential approximate point spectrum

中图分类号:

O177.1

左飞, 申俊丽. k-拟-*-A(ｎ)算子的性质[J]. 数学季刊, 2012, 27(3): 375-381.

ZUO Fei, SHEN Jun-li. The Properties of k-quasi-∗-A(n) Operator[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(3): 375-381.

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