Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PROPERTIES OF A κTH ROOT OF A HYPONORMAL OPERATOR

  • Ko, Eun-Gil (Department of Mathematics, Ewha Women’s University)
  • Published : 2003.11.01
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Abstract

In this paper, we study some properties of (equation omitted) (defined below). In particular we show that an operator T $\in$(equation omitted) satisfying the translation invariant property is hyponormal and an invertible operator T $\in$ (equation omitted) and its inverse T$^{-1}$ have a common nontrivial invariant closed set. Also we study some cases which have nontrivial invariant subspaces for an operator in (equation omitted).

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References

  1. J. Funct. Anal. v.128 Hypercyclic and cyclic vectors S.Ansari https://doi.org/10.1006/jfan.1995.1036
  2. Theory of generalized spectral operators I.Colojoara;C.Foias
  3. Subnormal operators J.Conway
  4. Arch. Math. v.52 Invariant subspaces for subscalar operators J.Eschmeier https://doi.org/10.1007/BF01237569
  5. A Hilbert space problem book P.R.Halmos
  6. Ph.D Thesis, Univ. of Toronto Invariant closed sets for linear operators C.Kitai
  7. Glasgow Math. J. v.41 Square roots of hyponormal operators M.Kim;E.Ko https://doi.org/10.1017/S0017089599000178
  8. Proc. Amer. Math. Soc. v.123 Algebraic and triangular n-hyponomal operators E.Ko
  9. Bull. Korean Math. Soc. v.33 no.1 On a Clary theorem E.Ko
  10. Lectures on hyponormal operators M.Martin;M.Putinar
  11. J. Operator Th. v.12 Hyponormal operators are subscalar M.Putinar
  12. Math. Zeit. v.116 An inequality for the area of hyponormal spectra C.R.Putnam https://doi.org/10.1007/BF01111839
  13. J. Math. Anal. Appl. v.34 On roots of normal operators H.Radjavi;P.Rosenthal https://doi.org/10.1016/0022-247X(71)90105-3
  14. Pacific J. Math. v.12 Hyponormal operators J.G.stampfli https://doi.org/10.2140/pjm.1962.12.1453

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  2. On Analytic Roots of Hyponormal Operators vol.14, pp.5, 2017, https://doi.org/10.1007/s00009-017-0998-3
  3. Continuity and Invariance of the Sacker–Sell Spectrum vol.28, pp.2, 2016, https://doi.org/10.1007/s10884-015-9515-1
  4. On Some Normality-Like Properties and Bishop's Property () for a Class of Operators on Hilbert Spaces vol.2012, 2012, https://doi.org/10.1155/2012/975745