Strongly Irreducible Operators on Hilbert Space

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Abstract

Background. The Main Tools. The Irreducibility and Strong Irreducibility of Operators. The Strongly Irreducible Operator in Some Classes of Operators. The Spectral Pictures of Strongly Irreducible Operators and the Approximate Jordan Decomposition Theorem. Compact Perturbations of Strongly Irreducible Operators. Strongly Irreducible Operators in Nest Algebras. Some Other Results about Strongly Irreducible Operators. References.