Spectra for upper triangular linear relation matrices through local spectral theory

被引:0
作者
Teresa Álvarez
Sonia Keskes
机构
[1] University of Oviedo,Department of Mathematics
[2] University of Monastir,Department of Mathematics
[3] Higher Institute of Computer Science of Mahdia,Laboratory of Dynamic systems and Combinatorial, Faculty of Sciences of Sfax
[4] University of Sfax,undefined
来源
Aequationes mathematicae | 2024年 / 98卷
关键词
Linear relation matrix; Fredholm spectrum; Drazin spectrum and SVEP; 47A06; 47A55;
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学科分类号
摘要
Let X and Y be Banach spaces. When A and B are linear relations in X and Y, respectively, we denote by MC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{C}$$\end{document} the linear relation in X×Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\times Y$$\end{document} of the form AC0B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \begin{array}{cc} A &{} C \\ 0 &{} B \\ \end{array} \right) $$\end{document}, where 0 is the zero operator from X to Y and C is a bounded operator from Y to X. In this paper, by using properties of the SVEP, we study the defect set (Σ(A)∪Σ(B))\Σ(MC)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\Sigma (A)\cup \Sigma (B))\backslash \Sigma (M_{C})$$\end{document}, where Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} is the spectrum, the approximate point spectrum, the surjective spectrum, the Fredholm spectrum, the Weyl spectrum, the Browder spectrum, the generalized Drazin spectrum and the Drazin spectrum.
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页码:399 / 422
页数:23
相关论文
共 40 条
  • [1] Álvarez T(2016)Left and Right-Atkinson linear relation matrices Mediterr. J. Math. 13 2039-2059
  • [2] Chamkha Y(2017)Left-right Fredholm and left-right Browder linear relations Filomat. 31 255-271
  • [3] Mnif M(2003)A note on the spectrum of an upper triangular operator matrix Proc. Amer. Math. Sco. 131 3083-3088
  • [4] Álvarez T(2017)Generalized Kato linear relations Filomat 31 1129-1139
  • [5] Fakhfakh F(2008)Browder spectra of upper triangular operator matrices J. Math. Anal. Appl. 193 477-484
  • [6] Mnif M(2013)Browder spectra of upper triangular matrix linear relations Publ. Math. Debrecen 82 569-590
  • [7] Barraa M(2002)Perturbations of spectra of operator matrices J. Operator Theory 48 467-486
  • [8] Boumazgour M(2001)On the generalized Drazin inverse and generalized resolvent Czech. Math. J. 51 617-634
  • [9] Benharrat M(2008)Essential point spectra of operator matrices trough local spectral theory J. Math. Anal. Appl. 338 285-291
  • [10] Álvarez T(2003)Local spectral theory for Jnt. J. Math. Sci. 42 2667-2672