Operators preserving orthogonality on Hilbert $\it{K}(H)$-modules

Authors

  • R. G. Sanati Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran
  • E. Ansari-piri Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran
  • M. Kardel Department of mathematics, University Campus 2, University of Guilan, P.O. Box 1914, Rasht, Iran. Current address: Department of mathematics, Islamic Azad University, Zabol Branch, Zabol, Iran

DOI:

Keywords:

Orthogonality preserving operators, adjoint of operators, isometry, Hilbert $\it{K(H)}$-module

Abstract

In this paper, we study the class of orthogonality preserving operators on a Hilbert $\it{K(H)}$-module $W$ and show that an operator $T$ on $W$ is orthogonality preserving if and only if it is orthogonality preserving on a special dense submodule of $W$. Then we apply this fact to show that an orthogonality preserving operator $T$ is normal if and only if $T^*$ is orthogonality preserving.

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Published

2019-06-25

Issue

Vol. 25 No. 2 (2019)

Section

Articles

How to Cite

Sanati, R. G., et al. “Operators Preserving Orthogonality on Hilbert $\it{K}(H)$-Modules”. Methods of Functional Analysis and Topology, vol. 25, no. 2, June 2019, pp. 189-94, https://zen.imath.kiev.ua/index.php/mfat/article/view/722.