Translation preserving operators on locally compact abelian groups
Functional Analysis
2019-10-31 v1
Abstract
We study translation preserving operators, that is operators commuting with translations by a closed subgroup of a locally compact abelian group. We show that there is a one to one correspondence between these operators and range operators. Furthermore, we obtain a necessary condition for a translation preserving operator to be Hilbert Schmidt or of finite trace in terms of its range operator.
Cite
@article{arxiv.1910.13514,
title = {Translation preserving operators on locally compact abelian groups},
author = {M. Mortazavizadeh and R. Raisi Tousi},
journal= {arXiv preprint arXiv:1910.13514},
year = {2019}
}