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Normal operators similar to irreducible operators. (English) Zbl 0813.47020

Summary: A complete characterization of normal operators which are similar to irreducible operators and some related results are given.

MSC:

47A65 Structure theory of linear operators
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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References:

[1] Gilfeather, F.,Strong irreducibility of operators, Indiana U. Math. J.,22 (1972), 393–397. · Zbl 0277.47018 · doi:10.1512/iumj.1973.22.22032
[2] Herrero, D. A., Approximation of Hilbert space operators, vol I, 2nd Ed., Pitman Research Notes in Math. Series, Longman, Essex, 1989.
[3] Lambert, A.,Strictly cyclic operator algebras, Pacific J. Math.,39 (1971), 717–727. · Zbl 0213.40701 · doi:10.2140/pjm.1971.39.717
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