Taiwanese Journal of Mathematics

SHIFT PRESERVING OPERATORS ON LOCALLY COMPACT ABELIAN GROUPS

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.

Article information

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

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406415

Digital Object Identifier
doi:10.11650/twjm/1500406415

Mathematical Reviews number (MathSciNet)
MR2880385

Zentralblatt MATH identifier
1275.47018

Citation

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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