Localization of operator-valued frames
Functional Analysis
2025-05-29 v2
Abstract
We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of an operator-valued frame is preserved by its canonical dual. Moreover, we show that the series associated to the perfect reconstruction of an operator-valued frame converges not only in the underlying Hilbert space, but also in a whole class of associated (quasi-)Banach spaces. Finally, we apply our results to irregular Gabor g-frames.
Cite
@article{arxiv.2503.24170,
title = {Localization of operator-valued frames},
author = {Lukas Köhldorfer and Peter Balazs},
journal= {arXiv preprint arXiv:2503.24170},
year = {2025}
}