대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권1호
  • /
  • Pages.233-246
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ANALYTIC EXTENSIONS OF M-HYPONORMAL OPERATORS

  • MECHERI, SALAH (COLLEGE OF SCIENCE DEPARTMENT OF MATHEMATICS TAIBAH UNIVERSITY) ;
  • ZUO, FEI (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HENAN NORMAL UNIVERSITY)
  • 투고 : 2014.11.07
  • 발행 : 2016.01.01
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초록

In this paper, we introduce the class of analytic extensions of M-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an M-hyponormal operator T is subscalar of order 2k + 2. Finally we obtain that an analytic extension of an M-hyponormal operator satisfies Weyl's theorem.

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참고문헌

  1. P. Aiena, Fredholm and Local Spectral Theory with Applications to Multipliers, Kluwer Academic Publishers, London, 2004.
  2. P. Aiena, E. Aponte, and E. Balzan, Weyl type theorems for left and right polaroid operators, Integral Equations Operator Theory 66 (2010), no. 1, 1-20. https://doi.org/10.1007/s00020-009-1738-2
  3. P. Aiena, M. Cho, and M. Gonzalez, Polaroid type operators under quasi-affinities, J. Math. Anal. Appl. 371 (2010), no. 2, 485-495. https://doi.org/10.1016/j.jmaa.2010.05.057
  4. S. K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970), 529-544. https://doi.org/10.1512/iumj.1971.20.20044
  5. S. Brown, Hyponormal operators with thick spectra have invariant subspaces, Ann. of Math. 125 (1987), no. 1, 93-103. https://doi.org/10.2307/1971289
  6. X. H. Cao, Analytically class A operators and Weyl's theorem, J. Math. Anal. Appl. 320 (2006), no. 2, 795-803. https://doi.org/10.1016/j.jmaa.2005.07.056
  7. M. Cho and Y. M. Han, Riesz idempotent and algebraically M-hyponormal operators, Integral Equations Operator Theory 53 (2005), no. 3, 311-320. https://doi.org/10.1007/s00020-004-1314-8
  8. H. R. Dowsow, Spectral Theory of Linear Operators, Academic Press, London, 1973.
  9. N. Dunford, A survey of the theory of spectral operators, Bull. Amer. Math. Soc. 64 (1958), 217-274. https://doi.org/10.1090/S0002-9904-1958-10219-0
  10. J. Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. (Basel) 52 (1989), no. 6, 562-570. https://doi.org/10.1007/BF01237569
  11. J. Eschmeier, K. B. Laursen, and M. M. Neumann, Multipliers with natural local spectra on commutative Banach algebras, J. Funct. Anal. 138 (1996), no. 2, 273-294. https://doi.org/10.1006/jfan.1996.0065
  12. J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves, London Mathematical Society Monographs, No. 10, Clarendon Press, Oxford, 1996.
  13. 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
  14. J. S. Han, S. H. Lee, and W. Y. Lee, On M-hyponormal weighted shifts, J. Math. Anal. Appl. 286 (2003), no. 1, 116-124. https://doi.org/10.1016/S0022-247X(03)00456-6
  15. R. E. Harte, Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. 85A (1985), 151-176.
  16. R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Dekker, New York, 1988.
  17. J. C. Hou and X. L. Zhang, On the Weyl spectrum: Spectral mapping theorem and Weyl's theorem, J. Math. Anal. Appl. 220 (1998), no. 2, 760-768. https://doi.org/10.1006/jmaa.1997.5897
  18. K. B. Laursen and M. M. Neumann, Automatic continuity of intertwining linear operators on Banach spaces, Rend. Circ. Mat. Palermo 40 (1991), no. 2, 325-341. https://doi.org/10.1007/BF02845071
  19. K. B. Laursen, An Introduction to Local Spectral Theory, London Math. Soc. Monogr. (N.S) 20, Clarendon Press, Oxford, 2000.
  20. W. Y. Lee, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), no. 1, 131-138. https://doi.org/10.1090/S0002-9939-00-05846-9
  21. S. Mecheri, Bishop's property, SVEP and Dunford property (C), Electron. J. Linear Algra 23 (2012), 523-529.
  22. S. Mecheri, Bishop's property and Riesz idempotent for k-quas-paranormal operators, Banach J. Math. Anal. 6 (2012), no. 1, 147-154. https://doi.org/10.15352/bjma/1337014673
  23. S. Mecheri, Isolated points of spectrum of k-quasi--class A operators, Studia Math. 208 (2012), no. 1, 87-96. https://doi.org/10.4064/sm208-1-6
  24. S. Mecheri, On k-quasi-M-hyponormal operators, Math. Inequal. Appl. 16 (2013), no. 3, 895-902.
  25. K. K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212.
  26. M. Oudghiri, Weyl's and Browder's theorems for operators satisfying the SVEP, Studia Math. 163 (2004), no. 1, 85-101. https://doi.org/10.4064/sm163-1-5
  27. M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385-395.
  28. M. Putinar, Hyponormal operators and eigendistribution, Advances in invariant subspaces and other results of operator theory (Timioara and Herculane, 1984), 249-273, Oper. Theory Adv. Appl., 17, Birkhuser, Basel, 1986.
  29. M. Putinar, Quasisimilarity of tuples with Bishop's property ($\beta$), Integral Equations Operator Theory 15 (1992), no. 6, 1047-1052. https://doi.org/10.1007/BF01203128