Weyl type theorems for unbounded class-A operators View Full Text


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Article Info

DATE

2017-01-20

AUTHORS

Anuradha Gupta, Karuna Mamtani

ABSTRACT

The study of Weyl’s theorem and properties has been extended from the class of hermitian operators to the class of hyponormal and Toeplitz operator and several other non-normal classes. However, so far, this study has been limited to the bounded operators. In this paper, we introduce the class of unbounded class-A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} operators and study Weyl-type theorems and properties for this class under certain condition. Certain relations have been established between the isolated spectral points with the Weyl spectrum and the B-Weyl spectrum. Also, for bounded operators, some variants of the Weyl’s Theorem imply the others. In the case of unbounded class-A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} operators, several of those variants of the Weyl’s theorem have been shown to be equivalent. More... »

PAGES

745-754

References to SciGraph publications

  • 1909-12. Über beschränkte quadratische formen, deren differenz vollstetig ist in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 1
  • 1970-09. Spectral analysis using ascent, descent, nullity and defect in MATHEMATISCHE ANNALEN
  • 1966-02. Theorems on ascent, descent, nullity and defect of linear operators in MATHEMATISCHE ANNALEN
  • 2016-06-07. B-Fredholm Properties of Closed Invertible Operators in MEDITERRANEAN JOURNAL OF MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1007/s13370-017-0479-7

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    http://dx.doi.org/10.1007/s13370-017-0479-7

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