Taiwanese Journal of Mathematics, ( ISI ), Volume (15), No (5), Year (2011-10) , Pages (1939-1955)

Title : ( Shift Preserving Operators on Locally Compact Abelian Groups )

Authors: Rajab Ali Kamyabi Gol , Reihaneh Raisi Tousi ,

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We investigate shift preserving operators on locally compact abelian groups. We show that there is a one-to-one correspondence between shift preserving operators and range operators on L2(G) where G is a locally compact abelian group. We conclude that a shift preserving operator has several properties in common with its associated range operator, especially compactness of one implies compactness of the other. Moreover, we obtain a necessary condition for a shift preserving operator to be Hilbert Schmidt or of finite trace in terms of its range function.

Keywords

, Shift invariant space, Range function, Shift preserving operator, Range operator, Locally compact abelian group, Compact operator, Hilbert Schmidt operator,
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@article{paperid:1024262,
author = {Kamyabi Gol, Rajab Ali and Raisi Tousi, Reihaneh},
title = {Shift Preserving Operators on Locally Compact Abelian Groups},
journal = {Taiwanese Journal of Mathematics},
year = {2011},
volume = {15},
number = {5},
month = {October},
issn = {1027-5487},
pages = {1939--1955},
numpages = {16},
keywords = {Shift invariant space; Range function; Shift preserving operator; Range operator; Locally compact abelian group; Compact operator; Hilbert Schmidt operator; Trace.},
}

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%0 Journal Article
%T Shift Preserving Operators on Locally Compact Abelian Groups
%A Kamyabi Gol, Rajab Ali
%A Raisi Tousi, Reihaneh
%J Taiwanese Journal of Mathematics
%@ 1027-5487
%D 2011

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