Weak $A$-frames and weak $A$-semi-frames
Functional Analysis
2020-12-17 v1
Abstract
After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator or, for short, a \emph{weak lower -semi-frame} and we study its properties. In particular, we compare it with that of lower atomic systems, introduced in \cite{GB}. We discuss duality properties and we suggest several possible definitions for weak -upper semi-frames. Concrete examples are presented.
Cite
@article{arxiv.2012.09101,
title = {Weak $A$-frames and weak $A$-semi-frames},
author = {Jean-Pierre Antoine and Giorgia Bellomonte and Camillo Trapani},
journal= {arXiv preprint arXiv:2012.09101},
year = {2020}
}