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On a generalization of the Jordan canonical form theorem on separable Hilbert spaces


Author: Rui Shi
Journal: Proc. Amer. Math. Soc. 140 (2012), 1593-1604
MSC (2010): Primary 47A65, 47A67; Secondary 47A15, 47C15
DOI: https://doi.org/10.1090/S0002-9939-2011-11513-2
Published electronically: December 20, 2011
MathSciNet review: 2869143
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Abstract: We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.


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  • 1. M. B. Abrahamse, Multiplication operators. Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977), pp. 17-36, Lecture Notes in Math., 693, Springer, Berlin, 1978. MR 0526530 (80b:47042)
  • 2. Edward A. Azoff, Borel measurability in linear algebra. Proc. Amer. Math. Soc. 42 (1974), 346-350. MR 0327799 (48:6141)
  • 3. E. Azoff, C. Fong and F. Gilfeather, A reduction theory for non-self-adjoint operator algebras. Trans. Amer. Math. Soc. 224 (1976), 351-366. MR 0448109 (56:6419)
  • 4. Y. Cao, J. Fang, and C. Jiang, $ K$-groups of Banach algebras and strongly irreducible decompositions of operators. J. Operator Theory 48 (2) (2002), 235-253. MR 1938796 (2004f:47003)
  • 5. John B. Conway, A course in functional analysis. Second edition. Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990. MR 1070713 (91e:46001)
  • 6. Kenneth R. Davidson, $ C^*$-algebras by example (English summary), Fields Institute Monographs, 6. American Mathematical Society, Providence, RI, 1996. MR 1402012 (97i:46095)
  • 7. M. Enomoto and Y. Watatani, Relative position of four subspaces in a Hilbert space. Adv. Math. 201 (2) (2006), 263-317. MR 2211531 (2009d:46044)
  • 8. M. Enomoto and Y. Watatani, Exotic indecomposable systems of four subspaces in a Hilbert space. Integral Equations and Operator Theory 59 (2) (2007), 149-164. MR 2345993 (2009g:47194)
  • 9. M. Enomoto and Y. Watatani, Indecomposable representations of quivers on infinite-dimensional Hilbert spaces. J. Funct. Anal. 256 (4) (2009), 959-991. MR 2488332 (2010c:47238)
  • 10. F. Gilfeather, Strong reducibility of operators. Indiana Univ. Math. J. 22 (4) (1972), 393-397. MR 0303322 (46:2460)
  • 11. P. Halmos, Irreducible operators. Michigan Math. J. 15 (1968), 215-223. MR 0231233 (37:6788)
  • 12. C. Jiang, Similarity classification of Cowen-Douglas operators. Canad. J. Math. 56 (4) (2004), 742-775. MR 2074045 (2006d:47037)
  • 13. C. Jiang, X. Guo and K. Ji, $ K$-group and similarity classification of operators. J. Funct. Anal. 225 (1) (2005), 167-192. MR 2149922 (2006c:47023)
  • 14. C. Jiang and K. Ji, Similarity classification of holomorphic curves. Adv. Math. 215 (2) (2007), 446-468. MR 2355596 (2008g:46081)
  • 15. C. Jiang and R. Shi, Direct integrals of strongly irreducible operators. J. Ramanujan Math. Soc. 26 (2) (2011), 165-180. MR 2816786
  • 16. C. Jiang and Z. Wang, The spectral picture and the closure of the similarity orbit of strongly irreducible operators. Integral Equations Operator Theory 24 (1) (1996), 81-105. MR 1366542 (97h:47011)
  • 17. C. Jiang and Z. Wang, Structure of Hilbert space operators. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006. MR 2221863 (2008j:47001)
  • 18. Z. Jiang and S. Sun, On completely irreducible operators. Front. Math. China 1 (4) (2006), 569-581. MR 2257195 (2007g:47003)
  • 19. H. Radjavi and P. Rosenthal, Invariant subspaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77. Springer-Verlag, New York-Heidelberg, 1973. MR 0367682 (51:3924)
  • 20. J. T. Schwartz, $ W^*$-algebras. Gordon and Breach, New York, 1967. MR 0232221 (38:547)

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Additional Information

Rui Shi
Affiliation: School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China
Email: littlestoneshg@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2011-11513-2
Keywords: Strongly irreducible operator, masa, direct integral
Received by editor(s): October 27, 2010
Received by editor(s) in revised form: December 18, 2010
Published electronically: December 20, 2011
Additional Notes: The author was supported in part by NSFC Grant #10731020 and NSFC Grant #10901046.
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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