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<p>A bounded linear operator on a complex Banach space is said to be polynomially compact if a non-zero polynomial of that operator is compact. In the present paper, the perturbation class, as well the commuting perturbation class, and the topological interior of the set of all bounded linear polynomially compact operators are completely described in the context of infinite-dimensional complex separable Hilbert spaces.</p>

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Perturbations on polynomially compact operators

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Khalid Souilah

摘要

A bounded linear operator on a complex Banach space is said to be polynomially compact if a non-zero polynomial of that operator is compact. In the present paper, the perturbation class, as well the commuting perturbation class, and the topological interior of the set of all bounded linear polynomially compact operators are completely described in the context of infinite-dimensional complex separable Hilbert spaces.