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<p>We provide a new type of proof for known or new Gohberg lemmas for pseudodifferential operators on Abelian locally compact groups X. We use <i>C</i>*-algebraic techniques, which also give spectral results to which the Gohberg lemma is just a corollary. These results extend most of those appearing in the literature in various directions. In particular, compactness or a Lie structure are not needed. The ideal of all the compact operators in L<sup>2</sup>(X) is replaced by all the ideals having a crossed product structure, which is a consistent generalization. We also indicate several new examples, mostly connected to specific behaviors of functions on the dual Ξ of X.</p>

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Gohberg Lemma and spectral results for pseudodifferential operators on locally compact Abelian groups

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Néstor Jara,
  • Marius Măntoiu

摘要

We provide a new type of proof for known or new Gohberg lemmas for pseudodifferential operators on Abelian locally compact groups X. We use C*-algebraic techniques, which also give spectral results to which the Gohberg lemma is just a corollary. These results extend most of those appearing in the literature in various directions. In particular, compactness or a Lie structure are not needed. The ideal of all the compact operators in L2(X) is replaced by all the ideals having a crossed product structure, which is a consistent generalization. We also indicate several new examples, mostly connected to specific behaviors of functions on the dual Ξ of X.