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Additive Mappings Preserving Fredholm Operators with Fixed Nullity or Defect

Authors
  • Zhang, Ruihan1
  • Shi, Weijuan1
  • Ji, Guoxing1
  • 1 Shaanxi Normal University, Xi’an, 710119, China , Xi’an (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 29, 2021
Volume
41
Issue
5
Pages
1670–1678
Identifiers
DOI: 10.1007/s10473-021-0516-3
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal X}$$\end{document} be an infinite-dimensional real or complex Banach space, and ℬ(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal B}({\cal X})$$\end{document} the Banach algebra of all bounded linear operators on X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal X}$$\end{document}. In this paper, given any non-negative integer n, we characterize the surjective additive maps on ℬ(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal B}({\cal X})$$\end{document} preserving Fredholm operators with fixed nullity or defect equal to n in both directions, and describe completely the structure of these maps.

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