Remarks on j−$j-$eigenfunctions of operators

David E. Edmunds and Jan Lang

Mathematische Nachrichten, 2023, vol. 296, issue 3, 1071-1086

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.

Date: 2023
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https://doi.org/10.1002/mana.202100417

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