江樵芬;钟怀杰;

• 1:福建师范大学数学与计算机科学学院

摘要(Abstract)：

设X,Y是给定的Banach空间,对A∈B(X),B∈B(Y),C∈B(Y,X),以MC记XY上的算子{A C/0 B}.利用局部谱理论的工具给出关于A,B成立σ*(Mc)=σ*(A)∪σ*(B)(σ*∈{αb,σw,σD})的一些充分条件,同时给出例子说明所给的充分条件不同于Djordjevic S.V.,Zguitti H.和Zhang Y.N.等人所给的充分条件.

关键词(KeyWords)： 算子矩阵;单值扩张性;Browder谱

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金资助项目(10771034);; 福建省自然科学基金资助项目(S0650009);; 福建省教育厅基金资助项目(JB07047)

作者(Authors): 江樵芬;钟怀杰;

参考文献(References)：

• [1]Djordjevic S V,Zguitti H.Essential point spectra of operator matrices through local spectral theory[J].Journalof Mathematical Analysis and Applications,2008,338:285-291.
• [2]Zhang Y N,Zhong H J,Lin L Q.Browder spectra and essential spectra for operator matrices[J].ActaMathematica Sinica,2008,24:947-954.
• [3]Benhida C,Zerouali E H,Zguitti H.Spectra of upper triangular operator matrices[J].Proc Amer Math Soc,2005,133:3013-3020.
• [4]Zhang S F,Zhong H J,Jiang Q F.Drazin spetrum of operator matrices on the Banach space[J].Linear Algebraand Its Application,2008,429:2067-2075.
• [5]钟怀杰.Banach空间结构与算子理想[M].北京:科学出版社,2005.
• [6]Djordjevic S V,Han Y M.A note on Weyl s theorem for operator matrices[J].PAMS,2003(27):2543-2547.
• [7]Duggal B P.Upper triangular operators with SVEP:spectral properties[J].Filomat,2007(21):25-37.
• [8]江樵芬,陈晓玲,钟怀杰.关于算子的黎斯点[J].福建师范大学学报:自然科学版,2006(2):5-10.
• [9]Djordjevic S V,Dragan S.Perturbations of spectra of operator matrices[J].J Operator Theory,2002(48):467-486.
• [10]Schmoeger C.On isolated points of the spectrum of a bounded linear operator[J].Proc Amer Math Soc,1993(117):715-719.
• [11]邹承祖.线性算子的谱分解理论[M].长春:吉林大学出版社,1987.
• [12]Finch J K.The single-ralued extension property on a Banach space[J].Pacific J Math,1975(58):61-69.