IJPAM: Volume 88, No. 4 (2013)

THE STABILITY PROPERTIES OF
STRONG INVARIANT APPROXIMATION PROPERTY

Kankeyanathan Kannan
Department of Mathematics and Statistics
University of Jaffna
Jaffna, SRI LANKA


Abstract. Let $G$ be a countable exact discrete group. $G$ has the strong invariant approximation property(SIAP) if and only if \begin{equation*} C^{\ast}_{u}(G,S)^{G} = C_{\lambda}^{\ast}(G)\otimes S \end{equation*} for any Hilbert space $\mathcal{H}$ and closed subspace $S\subseteq \mathcal{H}$. We shall use results of Haagerup and Kraus on the approximation property (AP) to investigate some permanence properties of the SIAP for discrete groups. This can be done most efficiently for exact groups. In this paper we describe that the stability properties of the SIAP property pass to semi direct products, and extensions for discrete exact groups.

Received: September 12, 2013

AMS Subject Classification: 20F65, 18G60

Key Words and Phrases: strong invariant approximation property, uniform Roe algebras, invariant approximation property

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DOI: 10.12732/ijpam.v88i4.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 4