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arXiv · 2105.06560

Remarks on j-eigenfunctions of operators

D. E. Edmunds·J. Lang
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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 $j-$eigenfunctions and $j-$% eigenvalues, such a representation is possible under certain conditions on $T$. Particular cases discussed include those in which $T$ can be factorised 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.

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D. E. Edmunds, J. Lang. 2021-05-13. Remarks on j-eigenfunctions of operators. https://arxiv.org/abs/2105.06560

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