New York Journal of Mathematics
Volume 7 (2001) 49-58


Peter A. Linnell and Michael J. Puls

Zero Divisors and Lp(G), II

Published: June 4, 2001
Keywords: zero divisor, free group, Fourier transform, radial function, free abelian group
Subject: Primary: 43A15; Secondary: 43A25, 42B99

Let G be a discrete group, let p ≧ 1, and let Lp(G) denote the Banach space {∑g∈ G ag g | ∑g∈ G |ag|p < ∞}. The following problem will be studied: Given 0 ≠ α ∈ CG and 0 ≠ β ∈ Lp(G), is α * β ≠ 0? We will concentrate on the case G is a free abelian or free group.

Author information

Peter A. Linnell:
Math, VPI, Blacksburg, VA 24061-0123

Michael J. Puls:
New Jersey City University, Jersey City, NJ 07305-1597