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<p>If a tuple of bounded operators have a common reducing subspace of finite dimension, its projective joint spectrum has an algebraic component. In general, the converse is not true and there might be algebraic components in the projective joint spectrum without corresponding common reducing subspaces. In this paper, we give necessary and sufficient conditions for the occurrence of such correspondence.</p>

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Projective joint spectra and reducing subspace of operator tuples

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Michael I. Stessin

摘要

If a tuple of bounded operators have a common reducing subspace of finite dimension, its projective joint spectrum has an algebraic component. In general, the converse is not true and there might be algebraic components in the projective joint spectrum without corresponding common reducing subspaces. In this paper, we give necessary and sufficient conditions for the occurrence of such correspondence.