# Characterization of orthogonality preserving mappings in indefinite inner product spaces

Volume 26, Issue 1, pp 10--15
Publication Date: September 17, 2021 Submission Date: July 06, 2021 Revision Date: July 27, 2021 Accteptance Date: August 10, 2021
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### Authors

S. Sylviani - Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia. H. Garminia - Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia. P. Astuti - Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia.

### Abstract

In this article we study the class of mappings in indefinite inner product spaces which preserve orthogonality. We derive characterization of orthogonality preserving mappings in indefinite inner product spaces which is a generalization of characterization of orthogonality preserving mappings in inner product spaces proposed by Chmielinski [J. Chmielinski, J. Math. Anal. Appl., $\textbf{304}$ (2005), 158--169].

### Share and Cite

##### ISRP Style

S. Sylviani, H. Garminia, P. Astuti, Characterization of orthogonality preserving mappings in indefinite inner product spaces, Journal of Mathematics and Computer Science, 26 (2022), no. 1, 10--15

##### AMA Style

Sylviani S., Garminia H., Astuti P., Characterization of orthogonality preserving mappings in indefinite inner product spaces. J Math Comput SCI-JM. (2022); 26(1):10--15

##### Chicago/Turabian Style

Sylviani, S., Garminia, H., Astuti, P.. "Characterization of orthogonality preserving mappings in indefinite inner product spaces." Journal of Mathematics and Computer Science, 26, no. 1 (2022): 10--15

### Keywords

• Orthogonality preserving mappings
• indefinite inner products spaces
• Krein spaces

•  15A86
•  47B49
•  47B50

### References

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• [2] J. Chmielinski, Linear mappings approximately preserving orthogonality, J. Math. Anal. Appl., 304 (2005), 158--169

• [3] I. Gohberg, P. Lancaster, L. Rodman, Indefinite Linear Algebra and Applications, Birkhauser Verlag, Basel (2005)

• [4] A. Saraei, M. Amyari, Orthogonality Preserving Mappings in Krein Spaces, J. Math. Anal., 10 (2019), 112--122

• [5] A. Saraei, M. Amyari, Approximately orthogonality preserving maps in Krein spaces, Aequationes Math., 94 (2020), 137--149

• [6] P. Wojcik, Operators preserving sesquilinear form, Linear Algebra Appl., 469 (2015), 531--538