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

### 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.

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

### Article Information

 Title Operators preserving orthogonality on Hilbert $\it{K}(H)$-modules Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 189-194 MathSciNet MR3978682 Milestones Received 24/01/2018; Revised 04/08/2018 Copyright The Author(s) 2019 (CC BY-SA)

### Authors Information

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

### Citation Example

R. G. Sanati, E. Ansari-piri, and M. Kardel, Operators preserving orthogonality on Hilbert $\it{K}(H)$-modules, Methods Funct. Anal. Topology 25 (2019), no. 2, 189-194.

### BibTex

@article {MFAT1173,
AUTHOR = {R. G. Sanati and E. Ansari-piri and M. Kardel},
TITLE = {Operators preserving orthogonality on Hilbert $\it{K}(H)$-modules},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {2},
PAGES = {189-194},
ISSN = {1029-3531},
MRNUMBER = {MR3978682},
URL = {http://mfat.imath.kiev.ua/article/?id=1173},
}

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