Localized Frames and Compactness
Functional Analysis
2015-08-05 v2
Abstract
We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers, Calderon-Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transform.
Cite
@article{arxiv.1409.5921,
title = {Localized Frames and Compactness},
author = {Fawwaz Batayneh and Mishko Mitkovski},
journal= {arXiv preprint arXiv:1409.5921},
year = {2015}
}