Samuel multiplicity and the structure of essentially semi-regular operators: A note on a paper of Fang  

作　　者：ZENG QingPing ZHONG HuaiJie WU ZhenYing 

机构地区：[1]School of Mathematics and Computer Science, Fujian Normal University [2]Fuzhou Strait Vocation Technological College

出　　处：《Science China Mathematics》2013年第6期1213-1231,共19页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11171066);Specialized Research Fund for the Doctoral Program of Higher Education (Grant Nos. 2010350311001 and 20113503120003);Natural Science Foundation of Fujian Province (Grant Nos. 2011J05002 and 2012J05003);Foundation of the Education Department of Fujian Province (Grant No. JB10042)

摘　　要：Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang's 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang's paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang's 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ∈ C in an essentially semi-regular domain.Motivated by a paper of Fang （2009）, we study the Samuel multiplicity and the structure of es- sentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang＇s results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang＇s 4×4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang＇s paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang＇s 4× 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ∈C in an essentially semi-regular domain.

关 键 词：samuel multiplicity essentially semi-regular operators semi-Fredholm operators semi-regularoperators Kato decomposition 

分 类 号：O177[理学—数学]