Truncation Approximations and Spectral Invariant S

Authors: Xiaoman Chen Qin Wang Xianjin Wang

Publish Date: 2014/12/20

Volume: 21, Issue: 3, Pages: 555-574

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Abstract

In this paper we study band truncation approximations for operators in uniform Roe algebras of countable discrete groups Under conditions on certain growth rates for discrete groups we find large classes of dense subspaces of uniform Roe algebras whose elements can be approximated by their band truncations in the operator norm We apply these results to construct a nested family of spectral invariant Banach algebras on discrete groups For a group with polynomial growth the intersection of these Banach algebras is a spectral invariant dense subalgebra of the uniform Roe algebra For a group with subexponential growth we show that the Wiener algebra of the group is a spectral invariant dense subalgebra of the uniform Roe algebraThe authors wish to thank the referees for their huge amount of corrections explanations and valuable comments on the original version of this paper The authors are also very grateful to Taxas AM University for its support and hospitality during their visits The second author wishes to thank the Erwin Schrödinger International Institute for Mathematical Physics Universität Wien for its support and hospitality during his visit in April 2014 in the Workshop on “Geometry of Computation in Groups” The third author is also indebted to the China Scholarship Council for its support The authors are supported in part by NSFC No 11231002 11420101001 10901033 10971023

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