Title : ( SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS )
Authors: Rajab Ali Kamyabi Gol , Reihaneh Raisi Tousi ,
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Abstract
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, Trace.
@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.},
}
%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
