PreprintCC BY-NC-ND 4.0arXiv
Bi-atomic systems in Hilbert Spaces
Abstract
This paper, we introduce and study biatomic systems in Hilbert spaces, a natural generalization of classical atomic systems; this new concept allows us to represent bounded linear operators using two Bessel sequences simultaneously. In addition, we establish equivalent characterizations of these systems, study their relationship with Bessel biframes and demonstrate the stability of the class under natural operations: duality with respect to the adjunct, orthogonal projections, unit operators and concatenation.
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BibTeX
@misc{villar2026biatomic,
title = {{Bi-atomic systems in Hilbert Spaces}},
author = {Osmin Ferrer Villar and Jose Naranjo Martinez and Breiner Rivero Reyes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16031},
eprint = {2610.16031},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16031},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bi-atomic systems in Hilbert Spaces
AU - Osmin Ferrer Villar
AU - Jose Naranjo Martinez
AU - Breiner Rivero Reyes
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16031
UR - https://arxiv.org/abs/2610.16031
AB - This paper, we introduce and study biatomic systems in Hilbert spaces, a natural generalization of classical atomic systems; this new concept allows us to represent bounded linear operators using two Bessel sequences simultaneously. In addition, we establish equivalent characterizations of these systems, study their relationship with Bessel biframes and demonstrate the stability of the class under natural operations: duality with respect to the adjunct, orthogonal projections, unit operators and concatenation.
ER -