Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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k-TH ROOTS OF p-HYPONORMAL OPERATORS

  • DUGGAL BHAGWATI P. (REDWOOD GROVE) ;
  • JEON IN Ho (DEPARTMENT OF MATHMATHICS, EWHA WOMEN'S UNIVERSITY) ;
  • KO AND EUNGIL (DEPARTMENT OF MATHMATHICS, EWHA WOMEN'S UNIVERSITY)
  • Published : 2005.08.01
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Abstract

In this paper we prove that if T is a k-th root of a p­hyponormal operator when T is compact or T$^{n}$ is normal for some integer n > k, then T is (generalized) scalar, and that if T is a k-th root of a semi-hyponormal operator and have the property $\sigma$(T) is contained in an angle < 2$\pi$/k with vertex in the origin, then T is subscalar.

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References

  1. A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory 13 (1990), 307-315 https://doi.org/10.1007/BF01199886
  2. C. Apostol, Spectral decomposition and functional calculus, Rev. Roumaine Math. Pures Appl. 13 (1968), 1481-1528
  3. B. P. Duggal, Quasi-similar p-hyponormal operators, Integral Equations Operator Theory 26 (1996), 338-345 https://doi.org/10.1007/BF01306546
  4. J. Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. 52 (1989), 562-570 https://doi.org/10.1007/BF01237569
  5. M. Fujii, C. Himeji, and A. Matsumoto, Theorems of Ando and Saito for p-hyponormal operators, Math. Japonica 39 (1994), 595-598
  6. T. Furuta, Invitation to linear operators, Taylor & Francis, London and New York, 2001
  7. F. Gilfeather, Operator valued roots of abelian analytic functions, Pacific J. Math. 55 (1974), 127-148 https://doi.org/10.2140/pjm.1974.55.127
  8. M. Kim and E. Ko, Square roots of hyponormal operators, Glasg. Math. J. 41 (1999), 463-470 https://doi.org/10.1017/S0017089599000178
  9. E. Ko, On p-hyponormal operators, Proc. Amer. Math. Soc. 128 (2000), 775- 780
  10. K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Math. Soc. Monogr. (N.S.) 2000
  11. M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), 385-395
  12. D. Xia, Spectral Theory of Hyponormal Operators, Birkhauser Verlag, Boston, 1983