The Theorems of WEYL and Von Neumann on Hermitean Carleman Operators
Theorem 7.1. (Weyl-von Neumann): Given any hermitean operator A on L2, there exists a Hilbert-Schmidt operator X with arbitrarily small double-norm, such that A + X has a pure point spectrum; the set of limit points of the spectra of A and of A + X is identical.
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