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Zero divisors and $L^p(G)$

Author: Michael J. Puls
Journal: Proc. Amer. Math. Soc. 126 (1998), 721-728
MSC (1991): Primary 43A15; Secondary 43A25, 42B99
MathSciNet review: 1415362
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Abstract: Let $G$ be a discrete group, $\mathbb{C}G$ the group ring of $G$ over $\mathbb{C}$ and $L^p(G)$ the Lebesgue space of $G$ with respect to Haar measure. It is known that if $G$ is torsion free elementary amenable, $0\ne \alpha\in \mathbb{C}G$ and $0\ne \beta\in L^2(G)$, then $\alpha*\beta\ne 0$. We will give a sufficient condition for this to be true when $p>2$, and in the case $G=\mathbb{Z}^n$ we will give sufficient conditions for this to be false when $p>2$.

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Additional Information

Michael J. Puls
Affiliation: Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

Keywords: Group ring, $p$-zero divisor, uniform nonzero divisor, Fourier transform, regular point, manifold of finite type
Received by editor(s): November 29, 1994
Received by editor(s) in revised form: July 15, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society

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