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http://dx.doi.org/10.4134/CKMS.2015.30.3.169

NUMERICAL RANGE AND SOT-CONVERGENCY  

ABDOLLAHI, ABDOLAZIZ (Department of Mathematics College of Sciences Shiraz University)
HEYDARI, MOHAMMAD TAGHI (Department of Mathematics College of Sciences Yasouj University)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.3, 2015 , pp. 169-176 More about this Journal
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
numerical range; composition operator; Hardy space;
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1 A. Abdollahi, The numerical range of a composition operator with conformal automorphism symbol, Linear Algebra Appl. 408 (2005), 177-188.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI
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.   DOI   ScienceOn
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.