On Eigenvalues and Boundary Curvature of the Numerical Rang of Composition Operators on Hardy Space


For a bounded linear operator A on a Hilbert space H, let M(A) be the smallest possible constant in the inequality . Here, p is a point on the smooth portion of the boundary of the numerical range of A. is the radius of curvature of at this point and  is the distance from p to the spectrum of A. In this paper, we compute the M(A) for composition operators on Hardy space H2.

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Heydari, M. (2015) On Eigenvalues and Boundary Curvature of the Numerical Rang of Composition Operators on Hardy Space. Advances in Pure Mathematics, 5, 333-337. doi: 10.4236/apm.2015.56032.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Gustafon, K.E. and Rao, K.M. (1997) The Numerical Range, The Field of Values of Linear Operators and Matrices. Springer, New York.
[2] Mathias, R. (1997).
[3] Caston, L., Savova, M., Spitkovsky, I. and Zobin, N. (2001) On Eigenvalues and Boundary Curvature of the Numerical Range. Linear Algebra and Its Applications, 322, 129-140.
[4] Littlewood, J.E. (1925) On Inequalities in the Theory of Functions. Proceedings London Mathematical Society, 23, 481-519.
[5] Shapiro, J.H. (1993) Composition Operators and Classical Function Theory. Springer-Verlag, New York.
[6] Cowen, C.C. and Maccluer, B.D. (1995) Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton.
[7] Rudin, W. (1987) Real and Complex Analysis. 3rd Edition, McGraw-Hill, New York.
[8] Bourdon, P.S. and Shapiro, J.H. (2000) The Numerical Range of Automorphic Composition Operators. Journal of Mathematical Analysis and Applications, 251, 839-854.
[9] Matache, V. (2001) Numerical Ranges of Composition Operators. Linear Algebra and Its Applications, 331, 61-74.
[10] Nordgren, E. (1968) Composition Operators. Canadian Journal of Mathematics, 20, 442-449.
[11] Abdollahi, A. (2005) The Numerical Range of a Composition Operator with Conformal Automorphism Symbol. Linear Algebra and Its Applications, 408, 177-188.
[12] Rodman, L. and Spitkovsky, I.M. (2008) On Generalized Numerical Ranges of Quadratic Operators. Operator Theory: Advances and Applications, 179, 241-256.

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