대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제28권4호
  • /
  • Pages.741-750
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  • 2013
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON QUASI-A(n, κ) CLASS OPERATORS

  • Lee, Mi Ryeong (Department of Mathematics Kyungpook National University) ;
  • Yun, Hye Yeong (Department of Mathematics Kyungpook National University)
  • 투고 : 2012.01.16
  • 발행 : 2013.10.31
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초록

To study the operator inequalities, the notions of class A operators and quasi-class A operators are developed up to recently. In this paper, quasi-$A(n,{\kappa})$ class operator for $n{\geq}2$ and ${\kappa}{\geq}0$ is introduced as a new notion, which generalizes the quasi-class A operator. We obtain some structural properties of these operators. Also we characterize quasi-$A(n,{\kappa})$ classes for n and ${\kappa}$ via backward extension of weighted shift operators. Finally, we give a simple example of quasi-$A(n,{\kappa})$ operators with two variables.

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참고문헌

  1. 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), no. 4, 497-508. https://doi.org/10.1007/s00020-004-1332-6
  2. B. Duggal, I. Jeon, and C. Kubrusly, Contractions satisfying the absolute value property $|A|^2{\leq}|A^2|$, Integral Equations Operator Theory 49 (2004), no. 2, 141-148. https://doi.org/10.1007/s00020-002-1202-z
  3. T. Furuta, Invitation to Linear Operators, Taylor and Francis Inc. London and New York, 2001.
  4. T. Furuta, M. Ito, and T. Yamazaki, A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1 (1998), no. 3, 389-403.
  5. F. Gao and X. Fang, On k-quasiclass A operators, J. Inequal. Appl. 2009 (2009), Article ID 921634, 10 pages.
  6. J. K. Han, H. Y. Lee, and W. Y. Lee, Invertible completions of 2 ${\times}$ 2 upper triangular operator matrices, Proc. Amer. Math. Soc. 128 (2000), no. 1, 119-123. https://doi.org/10.1090/S0002-9939-99-04965-5
  7. F. Hansen, An operator inequality, Math. Ann. 246 (1980), no. 3, 249-250. https://doi.org/10.1007/BF01371046
  8. T. Hoover, I. B. Jung, and A. Lambert, Moment sequences and backward extensions of subnormal weighted shifts, J. Aust. Math. Soc. 73 (2002), no. 1, 27-36. https://doi.org/10.1017/S1446788700008454
  9. M. Ito, On classes of operators generalizing class A and paranormality, Sci. Math. Jpn. 57 (2003), no. 2, 287-297.
  10. Z. Jablonski, I. B. Jung, and J. Stochel, Backward extensions of hyperexpansive operators, Studia Math. 173 (2006), no. 3, 233-257. https://doi.org/10.4064/sm173-3-2
  11. I. H. Jeon and I. H. Kim, On operators satisfying $T^{\ast}|T^2|T{\geq}T^{\ast}|T|^2T{\ast}$, Linear Algebra Appl. 418 (2006), no. 2-3, 854-862. https://doi.org/10.1016/j.laa.2006.02.040
  12. S. Jung, E. Ko, and M. Lee, On class A operators, Studia Math. 198 (2010), no. 3, 249-260. https://doi.org/10.4064/sm198-3-4
  13. A. Uchiyama and K. Tanahashi, On the Riesz idempotent of class A operators, Math. Inequal. Appl. 5 (2002), no. 2, 291-298.
  14. A. Uchiyama, K. Tanahashi, and J. Lee, Spectrum of class A(s, t) operators, Acta Sci. Math. (Szeged) 70 (2004), no. 1-2, 279-287.