Open Access

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


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.

Full Text

Article Information

TitleOperators preserving orthogonality on Hilbert $\it{K}(H)$-modules
SourceMethods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 189-194
MathSciNet MR3978682
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

Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley

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.


@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 = {},


Coming Soon.

All Issues