Translation preserving operators on locally compact abelian groups

M. Mortazavizadeh, R. Raisi Tousi

Published 2019-10-20Version 1

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.