Remarks on j−$j-$eigenfunctions of operators

Abstract

AbstractThe 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 eigenfunctions and 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.