Some Results on Frame Operators in 2-Hilbert Spaces
DOI :
https://doi.org/10.5269/bspm.82362Résumé
We investigate operator-theoretic aspects of frames in 2-Hilbert spaces. Frames associated with a
fixed vector are considered, and corresponding frame operators are introduced. The notions of zero operators,
equality of operators, and adjoint operators are extended from Hilbert spaces to the 2-Hilbert setting. It is
shown that frame operators are linear, bounded, positive, self-adjoint, and invertible in the 2-Hilbert sense.
For finite-dimensional 2-Hilbert spaces, matrix representations of frame operators are obtained. Canonical
dual frames and reconstruction formulas are also established.
Téléchargements
Publié
Numéro
Rubrique
Licence
© Boletim da Sociedade Paranaense de Matemática 2026
Cette œuvre est sous licence Creative Commons Attribution 4.0 International.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Comment citer
