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<p>In this paper, we investigate the isolated equivalence classes in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>S</mi> </math></EquationSource> </InlineEquation>-spectrum and their associated spectral projections in quaternionic right Hilbert spaces. We then characterize the Riesz points of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(S\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>S</mi> </math></EquationSource> </InlineEquation>-spectrum for a bounded right linear operator and establish a quaternionic analogue of Weyl’s theorem.</p>

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Riesz Points and Weyl’s Theorem in Quaternionic Setting

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Rachid Arzini,
  • Ali Jaatit

摘要

In this paper, we investigate the isolated equivalence classes in the \(S\) S -spectrum and their associated spectral projections in quaternionic right Hilbert spaces. We then characterize the Riesz points of the \(S\) S -spectrum for a bounded right linear operator and establish a quaternionic analogue of Weyl’s theorem.