Abstract
In this paper we study the spectral theory for the class of linear operators A ∞ defined on the so-called non-archimedean Hilbert space E ω by, A ∞:= D + F ∞ where D is an unbounded diagonal linear operator and F ∞:= Σ k=1 ∞ u k ⊗ v k is an operator of infinite rank on E ω .
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