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 $L^2(G)$ 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.
Citation
R. A. Kamyabi Gol. R. Raisi Tousi. "SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS." Taiwanese J. Math. 15 (5) 1939 - 1955, 2011. https://doi.org/10.11650/twjm/1500406415
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