Title : ( Translation Preserving Operators on Locally Compact Abelian Groups )
Authors: Mahdi Mortazavizadeh , Reihaneh Raisi Tousi , Rajab Ali Kamyabi Gol ,
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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. The last result is proved in the case that the subgroup is discrete or compact.
Keywords
, Locally compact abelian group, Multiplication preserving operator, Range function, Translation preserving operator, Range operator.
@article{paperid:1080378,
author = {Mortazavizadeh, Mahdi and Raisi Tousi, Reihaneh and Kamyabi Gol, Rajab Ali},
title = {Translation Preserving Operators on Locally Compact Abelian Groups},
journal = {Mediterranean Journal of Mathematics},
year = {2020},
volume = {17},
number = {4},
month = {July},
issn = {1660-5446},
keywords = {Locally compact abelian group; Multiplication preserving operator; Range function; Translation preserving operator; Range operator.},
}
%0 Journal Article
%T Translation Preserving Operators on Locally Compact Abelian Groups
%A Mortazavizadeh, Mahdi
%A Raisi Tousi, Reihaneh
%A Kamyabi Gol, Rajab Ali
%J Mediterranean Journal of Mathematics
%@ 1660-5446
%D 2020
