Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NUMERICAL RANGE AND SOT-CONVERGENCY

  • Received : 2014.11.07
  • Published : 2015.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

A sequence of composition operators on Hardy space is considered. We prove that, by numerical range properties, it is SOT-convergence but not converge.

Keywords

References

  1. A. Abdollahi, The numerical range of a composition operator with conformal automorphism symbol, Linear Algebra Appl. 408 (2005), 177-188. https://doi.org/10.1016/j.laa.2005.06.005
  2. P. S. Bourdon and J. H. Shapiro, The numerical range of automorphic composition operators, J. Math. Analy. Appl. 251 (2000), no. 2, 839-854. https://doi.org/10.1006/jmaa.2000.7072
  3. P. S. Bourdon and J. H. Shapiro, When is zero in the numerical range of a composition operator, Integr. Equ. Oper. Theory. 44 (2002), no. 4, 410-441. https://doi.org/10.1007/BF01193669
  4. C. C. Cowen and B. D. Maccluer, Composition Operators on Spaces of Analytic Fnctions, CRC Press, Boca Raton, 1995.
  5. K. E. Gustafon and K. M. Rao, The Numerical Range, the Field of Values of Linear Operators and Matrices, Springer, New York, 1997.
  6. P. R. Halmos, Hilbert Space Problem Book, Springer, New York, 1982.
  7. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
  8. J. E. Littlewood, On inequalities in the theory of functions, Proc. London Math. Soc. 23 (1925), 481-519.
  9. V. Matache, Numerical ranges of composition operators, Linear Algebra Appl. 331 (2001), no. 1-3, 61-74. https://doi.org/10.1016/S0024-3795(01)00262-2
  10. W. Rudin, Real and Complex Analysis, McGraw-Hill Book Co., New York, 1987.
  11. J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag. 1993.
  12. R. K. Singh and J. S. Manhas, Composition Operators on Function Spaces, North-Holland Publishing Co., Amsterdam, 1993.