Geodesic
Spectral Inclusion and C.N.E.
Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 883-887

Voir la notice de l'article provenant de la source Cambridge University Press

1. An n-tuple S = (S 1, ..., Sn ) of commuting bounded linear operators on a Hilbert space H is said to have commuting normal extension if and only if there exists an n-tuple N = (N 1, ..., Nn ) of commuting normal operators on some larger Hilbert space K ⊃ H with the restrictions Ni|H = Si, i = 1, ..., n. If we take the minimal reducing subspace of N containing H, then N is unique up to unitary equivalence and is called the c.n.e. of S. (Here J denotes the multi-index (j 1, ..., jn ) of nonnegative integers and N *J = N 1 *jl ... Nn *jn and we emphasize that c.n.e. denotes minimal commuting normal extension.) If n = 1, then S 1 = S is called subnormal and N 1 = N its minimal normal extension (m.n.e.). 
Lubin, A. R. Spectral Inclusion and C.N.E.. Canadian journal of mathematics, Tome 34 (1982) no. 4, pp. 883-887. doi: 10.4153/CJM-1982-060-3
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[1] 1. Abrahamse, M. B., Commuting subnormal operators, Ill. J. Math. 22 (1978), 171–176. Google Scholar

[2] 2. Arveson, W., Subalgebras of C*-algebras II, Acta Math. 128 (1972), 271–308. Google Scholar

[3] 3. Bastian, J. J., A decomposition of weighted translation operators, Trans. Math. Soc. 224 (1976). Google Scholar

[4] 4. Bram, J., Subnormal operators, Duke Math. J. 22 (1955), 75–94. Google Scholar

[5] 5. Bunce, J., and Deddens, J., On the normal spectrum of a subnormal operator, Proc. Amer. Math. Soc. 63 (1977), 107–110. Google Scholar

[6] 6. Curto, R. E., Spectral inclusion for doubly commuting subnormal n-tuples, (preprint). Google Scholar

[7] 7. Dixmier, J., Les algebres d'operateurs dans l'espace Hilbertien (Gauthier-Villars, Paris, 1969). Google Scholar

[8] 8. Halmos, P. R., Normal dilations and extensions of operators, Summa. Brasil. Math. 2 (1950), 125–134. Google Scholar

[9] 9. Halmos, P. R., A Hilbert space problem book (Van Nostrand, Princeton, 1967). Google Scholar

[10] 10. Hastings, W., Commuting subnormal operators simultaneously quasisimilar to unilateral shifts, Ill. J. Math. 22 (1978), 506–519. Google Scholar

[11] 11. Janas, J., Lifting commutants of subnormal operators and spectral inclusion, Bull. Acad. Polon. 26 (1978). Google Scholar

[12] 12. Ito, T., On the commutative family of subnormal operators, J. Fac. Sci. Hokkaido, Sec. I 14 (1958), 1–15. Google Scholar

[13] 13. Lubin, A. R., Weighted shifts and products of subnormal operators, Ind. U. Math. J. 26 (1977), 839–845. Google Scholar

[14] 14. Lubin, A. R., A subnormal semigroup without normal extension, Proc. Amer. Math. Soc. 68 (1978), 133–135. Google Scholar

[15] 15. Lubin, A. R., Extensions of commuting subnormals, Lecture Notes in Math. 693 (Springer- Verlag), 115–128. Google Scholar

[16] 16. Waelbroeck, L., Le calcule symbolique dans les algebras commutatives, J. Math. Pures Appl. 33 (1954), 147–186. Google Scholar

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