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<p>The article [Chen, X., Wang, X., Wang, Q.: Truncation approximations and spectral invariant subalgebras in uniform Roe algebras of discrete groups. <i>J. Fourier Anal. Appl.</i>, <b>21</b>, 555–574 (2015)] investigated spectral subalgebras of the uniform Roe algebra, although their Theorem 4.7 on spectral invariance contains a gap. To address this gap, we construct a class of Fréchet subalgebras using polynomial growth weights and prove that these algebras are not only spectrally invariant but also dense in the uniform Roe algebra for groups of polynomial growth–thereby completing and extending the earlier results.</p>

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Spectral Invariance in Dense Subalgebras of Uniform Roe Algebras

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Siqi Jiang,
  • Xianjin Wang

摘要

The article [Chen, X., Wang, X., Wang, Q.: Truncation approximations and spectral invariant subalgebras in uniform Roe algebras of discrete groups. J. Fourier Anal. Appl., 21, 555–574 (2015)] investigated spectral subalgebras of the uniform Roe algebra, although their Theorem 4.7 on spectral invariance contains a gap. To address this gap, we construct a class of Fréchet subalgebras using polynomial growth weights and prove that these algebras are not only spectrally invariant but also dense in the uniform Roe algebra for groups of polynomial growth–thereby completing and extending the earlier results.