A Note on the Left Essential Spectra of Operator Matrices  

作　　者：Yuan LI Xiu Hong SUN Hong Ke DU 

机构地区：[1]College of Mathematics and Information Science, Shaanxi Normal University Xi'an 710062, P. R. China [2]Department of Basic Courses, Xi'an University of Science and Technology, Xi'an 710054, P. R. China [3]College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R, China

出　　处：《Acta Mathematica Sinica,English Series》2007年第12期2235-2240,共6页数学学报（英文版）

基　　金：NSF of China(10571113)

摘　　要：When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficient condition for Me to be left Fredholm for some C ∈ F（K, H） （C ∈ Inv（K, H）） is given, where F（K,H） and Inv（K, H） denote respectively, the set of Fredholm operators and the set of invertible operators of B（K, H）. In addition, we give a necessary and sufficient condition for Me to be left Fredholm for all C ∈ Inv（K, H）.When A ∈ B（H） and B ∈ B（K） are given, we denote by Me the operator matrix acting on the infinite dimensional separable Hilbert space H ＋ K of the form Me = （ A C O B）. In this paper, a necessary and sufficient condition for Me to be left Fredholm for some C ∈ F（K, H） （C ∈ Inv（K, H）） is given, where F（K,H） and Inv（K, H） denote respectively, the set of Fredholm operators and the set of invertible operators of B（K, H）. In addition, we give a necessary and sufficient condition for Me to be left Fredholm for all C ∈ Inv（K, H）.

关 键 词：left essential spectrum 2×2 operator matrix perturbations of spectra 

分 类 号：O151.21[理学—数学]