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<p>We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can be derived that such operators are almost always maximally noncompact in the sense that their ball measure of noncompactness coincides with their operator norm. We point out specifications of the universal principle to the case of the identity operator.</p>

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Maximal noncompactness of embeddings into Marcinkiewicz spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月16日

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  • Jan Malý,
  • Zdeněk Mihula,
  • Vít Musil,
  • Luboš Pick

摘要

We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can be derived that such operators are almost always maximally noncompact in the sense that their ball measure of noncompactness coincides with their operator norm. We point out specifications of the universal principle to the case of the identity operator.