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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.


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Article Information

TitleOperators preserving orthogonality on Hilbert $\it{K}(H)$-modules
SourceMethods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 189-194
MilestonesReceived 24/01/2018; Revised 04/08/2018
CopyrightThe 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


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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},
       URL = {http://mfat.imath.kiev.ua/article/?id=1173},
}


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