Group representations with empty residual spectrum

Details Group representations with empty residual spectrum Group representations with empty residual spectrum

2009-06-16

arxiv.org/abs/0906.2854v3

Int. Eq. Op. Th. 67 (2010), no. 1, 95--107

Mathematics

Functional Analysis

14 pages, preliminary version. Comments welcome. v2: some clarification and streamlining of the arguments; typos corrected and

Scientific paper

10.1007/s00020-010-1772-0

Let $X$ be a Banach space on which a discrete group $\Gamma$ acts by isometries. For certain natural choices of $X$, every element of the group algebra, when regarded as an operator on $X$, has empty residual spectrum. We show, for instance, that this occurs if $X$ is $\ell^2(\Gm)$ or the group von Neumann algebra $VN(\Gm)$. In our approach, we introduce the notion of a {\em surjunctive pair}, and develop some of the basic properties of this construction. The cases $X=\ell^p(\Gm)$ for $1

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