A note on property (WE) View Full Text


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Article Info

DATE

2017-03-20

AUTHORS

A. Liu

ABSTRACT

We investigate a new spectrum property (WE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${W_E}$$\end{document}), which extends the generalized Weyl theorem. Using the property of consistence in Fredholm and index, we establish for a bounded linear operator T defined on a Hilbert space sufficient and necessary conditions for which the property (WE)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(W_E)}$$\end{document} holds. We also explore conditions on Hilbert operators T and S so that property (WE)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(W_E)}$$\end{document} holds for T⊕S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T\oplus S}$$\end{document} . Moreover, we study the permanence of property (WE)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(W_E)}$$\end{document} under perturbations by power finite rank operators commuting with T and discuss the relation between property (WE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${W_E}$$\end{document}) and hypercyclic operators. More... »

PAGES

243-256

References to SciGraph publications

  • 1909-12. Über beschränkte quadratische formen, deren differenz vollstetig ist in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 1
  • 2008-12-22. Upper Triangular Operator Matrices, SVEP and Browder, Weyl Theorems in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • 1966. Perturbation theory for linear operators in NONE
  • 1966-02. Theorems on ascent, descent, nullity and defect of linear operators in MATHEMATISCHE ANNALEN
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    http://scigraph.springernature.com/pub.10.1007/s10474-017-0707-5

    DOI

    http://dx.doi.org/10.1007/s10474-017-0707-5

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