A characterization of orthogonality preserving operators

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎University of Guilan‎, ‎P.O‎. ‎Box 1914‎, ‎Rasht‎, ‎Iran.

2 Institute of Higher Education of ACECR(Academic Center of Education and Culture Research)‎, ‎Rasht branch‎, ‎Iran.

3 Department of Mathematics, University Campus 2, University of Guilan, P.O. Box 1914, Rasht, Iran

4 (As a faculty member of (and supported by) Islamic Azad University, Zabol branch, Zabol, Iran. )

Abstract

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogonality preserving operator‎.

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Main Subjects


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Volume 43, Issue 7
November and December 2017
Pages 2495-2505
  • Receive Date: 21 May 2017
  • Revise Date: 30 October 2017
  • Accept Date: 13 November 2017