Abstract
Let \( \mathcal{H} \) be a complex Hilbert space of dimension at least 3, and let \( \mathcal{B}(\mathcal{H}) \) denote the algebra of all bounded linear operators on \( \mathcal{H} \). Based on results by Molnar, this paper revisits the problem addressed in [18], which characterizes surjective maps \( \phi: \mathcal{B}(\mathcal{H}) \to \mathcal{B}(\mathcal{H}) \) that preserve the set of partial isometric operators in both directions. We focus exclusively on the linear case, rather than the more general additive case. Furthermore, we provide an alternative proof of the main result in [9] from a different point of view. Finally, we propose new directions for exploring maps that preserve higher-order partial isometric operators in both directions.
Full Text
Article Information
| Title | Linear maps preserving partial isometries and operator pairs whose products are projections |
| Source | Methods Funct. Anal. Topology, Vol. 32 (2026), no. 1, 18-24 |
| DOI | 10.31392/MFAT-npu26_1.2026.03 |
| Milestones | Received 18/05/2025; Revised 04/11/2025 |
| Copyright | The Author(s) 2026 (CC BY-SA) |
Authors Information
Mohamed Amine Aouichaoui
Department of Mathematics, University of Monastir, Faculty of Sciences of Monastir, Monastir, 5019, Tunisia
Citation Example
Mohamed Amine Aouichaoui, Linear maps preserving partial isometries and operator pairs whose products are projections, Methods Funct. Anal. Topology 32
(2026), no. 1, 18-24.
BibTex
@article {MFAT2208,
AUTHOR = {Mohamed Amine Aouichaoui},
TITLE = {Linear maps preserving partial isometries and operator pairs whose products are projections},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {32},
YEAR = {2026},
NUMBER = {1},
PAGES = {18-24},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1.2026.03},
URL = {https://mfat.imath.kiev.ua/article/?id=2208},
}
