Injective Convolution Operators on l8(G) are Surjective
- Autores: Yemon Choi
- Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 447-452
- Idioma: inglés
- DOI: 10.4153/cmb-2010-053-5
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Resumen
Let G be a discrete group and let f ? l1(G). We observe that if the natural convolution operator ?f: l8(G)? l8(G) is injective, then f is invertible in l1(G). Our proof simplifies and generalizes calculations in a preprint of Deninger and Schmidt by appealing to the direct finiteness of the algebra l1(G). We give simple examples to show that in general one cannot replace l8 with lp, 1 = p < 8, nor with L8(G) for nondiscrete G. Finally, we consider the problem of extending the main result to the case of weighted convolution operators on G, and give some partial results.
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