文献类型：期刊文献

中文题名：The Properties of k-quasi-＊-A（n） Operator

英文题名：The Properties of k-quasi-＊-A（n） Operator

作者：zuo fei[1];SHEN Jun-li[2]

第一作者：zuo fei

机构：[1]College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007,China;[2]Department of Mathematics, Xinxiang University, Xinxiang 453000, China

第一机构：College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007,China

年份：2012

卷号：27

期号：3

起止页码：375-381

中文期刊名：数学季刊：英文版

外文期刊名：Chinese Quarterly Journal of Mathematics

收录：CSTPCD;;CSCD:【CSCD2011_2012】；

基金：Supported by the Natural Science Foundation of the Department of Education of Henan Province（12B110025, 102300410012）

语种：英文

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

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

摘要：An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+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.
An operator T is called k-quasi-＊-A（n） operator, if T＊k｜T1＋n｜2/（1＋n）Tk ≥T＊k｜T＊ ｜2Tk , 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.