Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON OPERATORS WITH AN ABSOLUTE VALUE CONDITION

  • Jeon, In-Ho (Department of Mathematics Ewha Women′s University) ;
  • DUGGAL, B.P. (Department of Mathematics UAEU)
  • Published : 2004.07.01
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Abstract

Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.

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References

  1. Integr. Equat. Oper. Th. v.13 On p-hyponormal operators for 0〈 p〈 1 A.Aluthge https://doi.org/10.1007/BF01199886
  2. Acta Sci. Math. (Szeged) v.33 Operators with a norm condition T.Ando
  3. Proc. Amer. Math. Soc. v.17 Spectra of tensor products of operators A.Brown;C.Pearcy https://doi.org/10.2307/2035080
  4. Indiana Univ. Math. J. v.20 Weyl spectrum of an operator S.K.Berberian https://doi.org/10.1512/iumj.1970.20.20044
  5. Proc. Amer. Math. Soc. v.131 p-hyponormality is not translation-invariant Muneo Cho;J.I.Lee
  6. Bull. Austral. Math. Soc. v.21 Paranormal operators on Banach spaces N.N.Chourasia;P.B.Ramanujan https://doi.org/10.1017/S0004972700005980
  7. Glasg. Math. J. v.42 Tensor products of operators-strong stability and p-hyponormality B.P.Duggal https://doi.org/10.1017/S0017089500030068
  8. Comment. Math. Prace Mat. v.40 Weyl`s theorem in the class of algebraically p-hyponormal operators B.P.Duggal;S.V.Djordjevic
  9. Taylor & Francis Invitation to linear operators T.Furuta
  10. Sci. Math. v.1 A subclass of paranormal operators including class of log-hyponormal and several related classes T.Furuta;M.Ito;T.Yamazaki
  11. Proc. Amer. Math. Soc. v.128 Weyl`s theorem holds for algebraically hyponormal operators Y.M.Han;W.Y.Lee https://doi.org/10.1090/S0002-9939-00-05741-5
  12. Invertibility and Singularity for Bounded Linear Operators R.E.Harte
  13. Trans. Amer. Math. Soc. v.349 Another note on Weyl`s theorem R.E.Harte;W.Y.Lee https://doi.org/10.1090/S0002-9947-97-01881-3
  14. Acta Math. Sinica (N.S.) v.9 On tensor products of operators Jin-chuan Hou https://doi.org/10.1007/BF02560050
  15. Tohoku Math. J. v.18 On a class of operators V.Istratescu;T.Saito;T.Yoshino https://doi.org/10.2748/tmj/1178243383
  16. Math. Inequal. Appl. v.2 Several properties on class A including p-hyponormal and log-hyponormal operators M.Ito
  17. Integr. Equat. Oper. Th. v.39 Weyl`s theorem and quasi-similarity I.H.Jeon https://doi.org/10.1007/BF01195818
  18. Pacific J. Math. v.157 Operators with finite ascent K.B.Laursen
  19. Proc. Amer. Math. Soc. v.125 Essential spectra through local spectral theory K.B.Laursen https://doi.org/10.1090/S0002-9939-97-03852-5
  20. An Introduction to Local Spectral Theory London Math. Soc. Monographs (N.S.) K.B.Laursen;M.M.Neumann
  21. Glasg. Math. J. v.38 A spectral mapping theorem for the Weyl spectrum W.Y.Lee;S.H.Lee https://doi.org/10.1017/S0017089500031268
  22. Illinois J. Math. v.21 On the Weyl spectrum(Ⅱ) K.K.Oberai
  23. J. Math. Res. Exposition v.7 Paranormal operators with countable spectrum are normal operators C.Qiu
  24. Lecture Notes in Mathematics v.247 Hyponormal Operators and Related Topics T.Saito
  25. Proc. Amer. Math. Soc. v.124 Seminormality of operators from their tensor products Jan Stochel
  26. Math. Inequal. Appl. v.4 Weyl`s theorem for class A operators A.Uchiyama
  27. Integr. Equat. Oper. Th. On the isolated points of spectrum of paranormal operators A.Uchiyama
  28. Nihonkai Math. J. v.14 An example of non-reducing eigenspace of a paranormal operators A.Uchiyama
  29. Spectral Theory of Hyponormal Operators D.Xia

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