Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON QUASI-CLASS A OPERATORS

  • Kim, In Hyoun (Department of Mathematics University of Incheon) ;
  • Duggal, B.P. (8 Redwood Grove Northfield Avenue) ;
  • Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
  • Received : 2011.05.09
  • Accepted : 2011.06.03
  • Published : 2011.06.30
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Abstract

Let $\mathcal{QA}$ denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality $T^*|T^2|T{\geq}T^*|T|^2T$. Let $f$ be an analytic function defined on an open neighbourhood $\mathcal{U}$ of ${\sigma}(T)$ such that $f$ is non-constant on the connected components of $\mathcal{U}$. We generalize a theorem of Sheth [10] to $f(T){\in}\mathcal{QA}$.

Keywords

Acknowledgement

Supported by : Korea Research Foundation

References

  1. S. L. Campbell and B. C. Gupta, On k-quasihyponormal operators, Math. Japon. 23(1978-79), 185-189.
  2. M. Cho and T. Yamazaki, An operator transform from class A to the class of hyponormal operators and its application, Integral Equations Operator Theory, 53(2005), 497-508. https://doi.org/10.1007/s00020-004-1332-6
  3. T. Furuta, Invitation to Linear Operators, Taylor and Francis, London (2001).
  4. 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
  5. M. Ito and T. Yamazaki, Relations between two inequalities $(B^{\frac{r}{2}}A^pB^{\frac{r}{2}})^{\frac{r}{p+r}}{\geq}B^r$ and $A^p{\geq}(A^{\frac{p}{2}}B^rA^{\frac{p}{2}})^{\frac{r}{p+r}}$ and their applications, Integral Equations Operator Theory, 44(2002), 442-450. https://doi.org/10.1007/BF01193670
  6. I. H. Jeon and I. H. Kim, On operators satisfying $T^*{\left|T^2\right|}{\geq}T^*{\left|T\right|}^2T$, Linear Algebra Appl. 418(2006), 854-862. https://doi.org/10.1016/j.laa.2006.02.040
  7. I. H. Jeon, I. H. Kim, K. Tanahashi and A. Uchiyama, Conditions implying self-adjointness of operators, Integral Equations Operator Theory, 61(2008), 549-557. https://doi.org/10.1007/s00020-008-1598-1
  8. I. H. Kim, The Fuglede-Putnam theorem for (p; k)-quasihyponormal operators, J. Inequal. Appl. (2006), 397-403.
  9. H. Radjavi and P. Rosenthal, On roots of normal operators, J. Math. Anal. Appl. 34(1971), 653-664. https://doi.org/10.1016/0022-247X(71)90105-3
  10. I. H. Sheth, On hyponormal operators, Proc. Amer. Math. Soc., 17(1966), 998- 1000. https://doi.org/10.1090/S0002-9939-1966-0196498-7
  11. J. P. Williams, Operators similar to their adjoints, Proc. Amer. Math. Soc. 20(1969), 121-123. https://doi.org/10.1090/S0002-9939-1969-0233230-5