Geodesic
On the Unitary Equivalence of Certain Classes of Non-Normal Operators. I
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 849-856

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The following (so-called unitary equivalence) problem is of paramount importance in the theory of operators: given two (bounded linear) operators A 1, A 2 on a (complex) Hilbert space , determine whether or not they are unitarily equivalent, i.e., whether or not there is a unitary operator U on such that U*A 1 U = A 2. For normal operators this question is completely answered by the classical multiplicity theory [7; 11]. Many authors, in particular, Brown [3], Pearcy [9], Deckard [5], Radjavi [10], and Arveson [1; 2], considered the problem for non-normal operators and have obtained various significant results. However, most of their results (cf. [13]) deal only with operators which are of type I in the following sense [12]: an operator, A, is of type I (respectively, II1, II∞, III) if the von Neumann algebra generated by A is of type I (respectively, II1, II∞, III). 
Tam, P. K. On the Unitary Equivalence of Certain Classes of Non-Normal Operators. I. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 849-856. doi: 10.4153/CJM-1971-095-9
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[1] 1. Arveson, W. B., Subalgebras of C*-algebras, Acta Math. 123 (1969), 142–224. Google Scholar

[2] 2. Arveson, W. B., Unitary invariants for compact operators, Bull. Amer. Math. Soc. 76 (1970), 88–91. Google Scholar

[3] 3. Brown, A., The unitary equivalence ofbinormal operators, Amer. J. Math. 76 (1954), 414–434. Google Scholar

[4] 4. Bures, D., Abelian subalgebras of von Neumann algebras, preprint (to be published in the Memoirs of Amer. Math. Soc.). Google Scholar

[5] 5. Deckard, D., Complete sets of unitary invariants for compact and trace-class operators, Acta Sci. Math. (Szeged) 28 (1967), 9–20. Google Scholar

[6] 6. Dixmier, J., Les algebres à'opérateurs dans l'espace Hilbertien, second edition (Gauthier- Villars, Paris, 1969). Google Scholar

[7] 7. Halmos, P. R., Introduction to Hilbert space and the theory of spectral multiplicity (Chelsea, New York, 1951). Google Scholar

[8] 8. Neumann, J. von and Murray, F. J., On rings of operators. III, Ann of Math. 1^1 (1940), 94–161. Google Scholar

[9] 9. Pearcy, C., A complete set of unitary invariants for operators generating finite W*-algebras of type I, Pacific J. Math. 12 (1962), 1405–1416. Google Scholar

[10] 10. Radjavi, H., Simultaneous unitary invariants for sets of bounded operators on a Hilbert space, Ph.D. Thesis, University of Minnesota, 1962. Google Scholar

[11] 11. Segal, I. E., Decompositions of operator algebras. II, Memoirs of Amer. Math. Soc, No. 9 (Amer. Math. Soc. Providence, R.I., 1951). Google Scholar

[12] 12. Suzuki, N., Isometries on Hilbert spaces, Proc. Japan Acad. 39 (1963), 435–438. Google Scholar

[13] 13. Suzuki, N., Algebraic aspects of non self-adjoint operators, Proc. Japan Acad. I±l (1965), 706–710. Google Scholar

[14] 14. Tarn, P. K., On the commutant of certain automorphism groups, pre-print. Google Scholar

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