Taiwanese Journal of Mathematics


R. A. Kamyabi Gol and R. 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 $L^2(G)$ 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.

Article information

Taiwanese J. Math., Volume 15, Number 5 (2011), 1939-1955.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary: 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

shift invariant space range function shift preserving operator range operator locally compact abelian group compact operator Hilbert Schmidt operator trace


Kamyabi Gol, R. A.; Raisi Tousi, R. SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS. Taiwanese J. Math. 15 (2011), no. 5, 1939--1955. doi:10.11650/twjm/1500406415. https://projecteuclid.org/euclid.twjm/1500406415

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