The Weyl-Von Neumann Theorem for Multipliers Of Some Af-Algebras
Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 322-330

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A well known theorem of Weyl-von Neumann asserts that if X is a self-adjoint operator acting on a separable Hilbert space, then there is a decomposition 1 = Σ en of the identity into finite rank projections so that we may write X = Σ ƛnen + y, where the ƛnare scalars and y is a compact operator with small norm. In other words, X can be approximately diagonalized.
Higson, Nigel; Rørdam, Mikael. The Weyl-Von Neumann Theorem for Multipliers Of Some Af-Algebras. Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 322-330. doi: 10.4153/CJM-1991-018-9
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