Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WEAK NORMAL PROPERTIES OF PARTIAL ISOMETRIES

  • Liu, Ting (Institute of Mathematics Jilin University) ;
  • Men, Yanying (Institute of Mathematics Jilin University) ;
  • Zhu, Sen (Department of Mathematics Jilin University)
  • Received : 2018.11.08
  • Accepted : 2019.03.04
  • Published : 2019.11.01
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Abstract

This paper describes when a partial isometry satisfies several weak normal properties. Topics treated include quasi-normality, subnormality, hyponormality, p-hyponormality (p > 0), w-hyponormality, paranormality, normaloidity, spectraloidity, the von Neumann property and Weyl's theorem.

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References

  1. S. Chavan and R. Curto, Weyl's theorem for pairs of commuting hyponormal operators, Proc. Amer. Math. Soc. 145 (2017), no. 8, 3369-3375. https://doi.org/10.1090/proc/13479
  2. L. A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285-288. http://projecteuclid.org/euclid.mmj/1031732778 https://doi.org/10.1307/mmj/1031732778
  3. J. B. Conway, A Course in Functional Analysis, second edition, Graduate Texts in Mathematics, 96, Springer-Verlag, New York, 1990.
  4. J. B. Conway, The Theory of Subnormal Operators, Mathematical Surveys and Monographs, 36, American Mathematical Society, Providence, RI, 1991. https://doi.org/10.1090/surv/036
  5. R. E. Curto and Y. M. Han, Weyl's theorem, a-Weyl's theorem, and local spectral theory, J. London Math. Soc. (2) 67 (2003), no. 2, 499-509. https://doi.org/10.1112/S0024610702004027
  6. R. E. Curto and Y. M. Han, Generalized Browder's and Weyl's theorems for Banach space operators, J. Math. Anal. Appl. 336 (2007), no. 2, 1424-1442. https://doi.org/10.1016/j.jmaa.2007.03.060
  7. S. R. Garcia and W. R. Wogen, Complex symmetric partial isometries, J. Funct. Anal. 257 (2009), no. 4, 1251-1260. https://doi.org/10.1016/j.jfa.2009.04.005
  8. P. R. Halmos, A Hilbert Space Problem Book, second edition, Graduate Texts in Mathematics, 19, Springer-Verlag, New York, 1982.
  9. P. R. Halmos and J. E. McLaughlin, Partial isometries, Pacific J. Math. 13 (1963), 585-596. http://projecteuclid.org/euclid.pjm/1103035746 https://doi.org/10.2140/pjm.1963.13.585
  10. Y. M. Han and W. Y. Lee, Weyl's theorem holds for algebraically hyponormal operators, Proc. Amer. Math. Soc. 128 (2000), no. 8, 2291-2296. https://doi.org/10.1090/S0002-9939-00-05741-5
  11. D. A. Herrero, Approximation of Hilbert Space Operators. Vol. I, Research Notes in Mathematics, 72, Pitman (Advanced Publishing Program), Boston, MA, 1982.
  12. C. Jiang and Z. Y. Wang, Structure of Hilbert Space Operators, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.
  13. P. Skoufranis, Numerical ranges of operators, unpublished preprint, http://pskoufra.info.yorku.ca/les/2016/07/Numerical-Range.pdf
  14. H. Weyl, Uber beschrankte quadratische formen, deren differenz, vollsteig ist, Rend. Circ. Mat. Palermo 27 (1909), 373-392. https://doi.org/10.1007/BF03019655
  15. S. Zhu, Approximate unitary equivalence of normaloid type operators, Banach J. Math. Anal. 9 (2015), no. 3, 173-193. https://doi.org/10.15352/bjma/09-3-13
  16. S. Zhu, Approximation of complex symmetric operators, Math. Ann. 364 (2016), no. 1-2, 373-399. https://doi.org/10.1007/s00208-015-1221-0