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algebraic operators Amer Apostol approximation argument Banach algebra C. M. Pearcy C*-algebra Calkin algebra clopen subset closed Closures of similarity compact operator compact perturbation compact quasinilpotent completely apparent contains Corollary 3.22 D. A. Herrero decomposition defined denotes dense denumerable easily seen exists a sequence finite dimensional space finite rank operator Foias fortiori Fredholm operator Furthermore given Hence Hilbert space infinite invariant subspace invertible isolated point Jordan operator L. A. Fialkow Lemma Math matrix n n=l nice Jordan nilpotent nilpotent operators nonempty norm numbers Observe obtain operator acting orthogonal projection PF(H proof of Theorem Pures et Appl quasinilpotent operators quasitriangular readily follows resp result Salinas satisfies semi-Fredholm semi-Fredholm operator similarity invariant similarity orbits spectral spectrum subset Theorem 5.1 triangular operators unitarily equivalent unitary operator universal operator vector Voiculescu whence