ALMOST NORMAL ELEMENTS
Huaxin Lin · International Journal of Mathematics · 1994
We show that, for any ε > 0, there exists δ > 0, such that for any finite matrix T with ||T|| ≤ 1 satisfies [Formula: see text] there is a normal operator N ∈ B (l2) such that [Formula: see text] where T∞ is the block diagonal operator with T on each diagonal block. We also show that, for any ε > 0, there exists δ > 0 such that for any element x with ||x|| ≤ 1 in any purely infinite simple C*-algebra A satisfies [Formula: see text] and a spectral condition, there is a normal element y ∈ A with finite spectrum [Formula: see text]