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<p>In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual <i>s</i>-numbers (e.g., approximation, Kolmogorov, and entropy numbers) fail to reveal finer structural properties, and one must instead consider concepts such as strict singularity and Bernstein numbers.</p>

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Notes on non-compact maps and the importance of Bernstein numbers

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • David E. Edmunds,
  • Jan Lang

摘要

In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual s-numbers (e.g., approximation, Kolmogorov, and entropy numbers) fail to reveal finer structural properties, and one must instead consider concepts such as strict singularity and Bernstein numbers.