[1]陈晓玲,钟怀杰.2*2上三角算子矩阵的左(右)Browder谱[J].华侨大学学报(自然科学版),2007,28(3):330-334.[doi:10.3969/j.issn.1000-5013.2007.03.028]
　CHEN Xiao-ling,ZHONG Huai-jie.Left(Right) Browder Spectra of 2*2 Upper Triangular Operator Matrices[J].Journal of Huaqiao University(Natural Science),2007,28(3):330-334.[doi:10.3969/j.issn.1000-5013.2007.03.028]
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2*2上三角算子矩阵的左(右)Browder谱()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第28卷
期数:
2007年第3期
页码:
330-334
栏目:
出版日期:
2007-07-20

文章信息/Info

Title:
Left(Right) Browder Spectra of 2*2 Upper Triangular Operator Matrices
文章编号:
1000-5013(2007)03-0330-05
作者:
陈晓玲; 钟怀杰
集美大学理学院; 福建师范大学数学与计算机科学学院 福建厦门361021; 福建福州350007
Author(s):
CHEN Xiao-ling1;  ZHONG Huai-jie2
1.School of Sciences, Jimei University, Xiamen 361021, China; 2.School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
关键词:
Banach空间;  算子矩阵;  左Browder谱;  右Browder谱
Keywords:
Banach space;  operator matrix;  left browder spectra;  right browder spectra
分类号:
O177.2
DOI:
10.3969/j.issn.1000-5013.2007.03.028
文献标志码:
A
摘要:
设X,Y是复的Banach空间,在一个上三角算子矩阵Mc=A C0 B∈B(XY)中,A∈B(X),B∈B(Y)是事先给定的,对于任意的C∈B(Y,X),Mc的左(右)Browder谱:lσb(Mc)={λ∈C:Mc)-λB+(XY)},B+(XY)={T∈Φ+(XY):asc(T)<∞},(rσb(Mc)={λ∈C:Mc)-λ■B-(XY)},B-(XY)={T∈Φ-(XY):des(T)<∞}).文中得到lσb(Mc)(rσb(Mc))与lσb(A)∪lσb(B)|rσb(A)∪rσb(B))之间存在有趣的填洞现象,即σ*(A)∪σ*(B)=σ*(Mc)∪W.其中,W是σ*(Mc)的某些洞的并σ*∈{lσb,rσb},并找出洞W的具体位置.
Abstract:
Let X and Y be complex Banach spaces,Mc be an upper triangular operator matrix with given A∈B(X),B∈B(Y) and any C∈B(YX),σlbMc={λ∈C:Mc)-λB+(XY)} be the left Brooder spectra and σrb(Mc)={λ∈C: Mc)-λB-(XY)} be the right Browder spectra of Mc,where B-(XY)={T∈Φ-(XY): des(T)<∞}.It is shown that the passage from σlb(Mc)(σrb(Mc)) to σlb(A)∪σlb(B)|σrb(A)∪σrb(B) is accomplished by filling holes,that is,there is an equality σ*(A)∪σ*(B)=σ*(Mc)∪W,where W is the union of certain holes in σ*(Mc) and σ*∈{σlb,σrb}.Furthermore,the exact location of W is found.

参考文献/References:

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[2] CAO X H, GUO M Z, MENG B. Weyl′s theorem for upper triangular operator matrices [J]. Linear Algebra and its Applications, 2005, (402):61-73.
[3] LEE W Y. Weyl spectra of operator matrices [J]. PAMS, 2000, (129):131-138.doi:10.1090/S0002-9939-00-05846-9.
[4] HWANG I S, LEE W Y. The boundedness below of 2*2 upper triangular operator matrices [J]. Integral Equations and Operator theory, 2001, (39):267-276.
[5] CAO X H, GUO M Z, MENG B. Semi-fredholm spectrum and Weyl′s theory for operator matrices [J]. Acta Mathematica Sinica, 2006, (22):169-178.
[6] 康威 J B, 吕以辇. 单复变函数 [M]. 上海:上海科学技术出版社, 1985.
[7] LEE W Y. A generalization of the punctured neighborhood theorem [J]. PAMS, 1993, (117):107-109.
[8] TAYLOR A E. Theorems on ascent, descent, nullity and defect of linear operators [J]. Mathematische Annalen, 1966, (163):18-49.doi:10.1007/BF02052483.
[9] 钟怀杰. 巴拿赫空间结构和算子理想 [M]. 北京:科学出版社, 2005.
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备注/Memo

备注/Memo:
国家自然科学基金资助项目(10471025); 福建省自然科学基金资助项目(S0650009)
更新日期/Last Update: 2014-03-23