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Remarks on j−$j-$eigenfunctions of operators

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  • David E. Edmunds
  • Jan Lang

Abstract

The paper is largely concerned with the possibility of obtaining a series representation for a compact linear map T acting between Banach spaces. It is known that, using the notions of j−$j-$eigenfunctions and j−$j-$ eigenvalues, such a representation is possible under certain conditions on T. Particular cases discussed include those in which T can be factorized through a Hilbert space, or has certain s‐numbers that are fast‐decaying. The notion of p‐compactness proves to be useful in this context; we give examples of maps that possess this property.

Suggested Citation

  • David E. Edmunds & Jan Lang, 2023. "Remarks on j−$j-$eigenfunctions of operators," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1071-1086, March.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:3:p:1071-1086
    DOI: 10.1002/mana.202100417
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