• Takagi, Hiroyuki ;
  • Miura, Takeshi ;
  • Takahasi, Sin-Ei
  • Published : 2003.11.01


For a weighted composition operator $uC_{\varphi}$ on C(X), we determine its essential norm and the constant for its Hyers-Ulam stability, in terms of the set $\varphi(\{x\;\in\;X\;:\;$\mid$u(x)$\mid$\;\geq\;r\})$ (r > 0).


weighted composition operator;essential norm;Hyers-Ulam stability;closed range


  1. Proc. Amer. Math. Soc. v.99 Compact and weakly compact composition operators on space of vector valued continuous functions R.K.Singh;W.H.Summers
  2. Bull. Korean Math. Soc. v.39 no.2 On the Hyers-Ulam stability of the Banach space-valued differential equation $\frak{y}^ '$ = $λ\frak{y}$ S.E.Takahasi;T.Miura;S.Miyajima
  3. J. Operator Theory v.19 Weighted composition operator on C(X, E) J.E.Jamison;M.Rajagopalan
  4. Ann. of Math. v.125 no.2;2 The essential norm of a composition operator J.H.Shapiro
  5. Tokyo J. Math. v.24 On the Hyers-Ulam stability of real continuous function valued differentiable map T.Miura;S.E.Takahasi;H.Choda
  6. Proc. Amer. Math. Soc. v.108 Compact weighted composition operators on Banach lattices W.Feldman
  7. Proc. Nat. Acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D.H.Hyers
  8. Problems in modern mathematics S.M.Ulam
  9. Introduction to functional analysis(2nd ed.) A.E.Taylor;D.C.Lay
  10. Tokyo J. Math. v.11 Compact weighted composition operators on function algebras H.Takagi
  11. Linear Operators Part Ⅰ N.Dunford;J.T.Schwartz
  12. Math. Nachr. v.258 Hyers-Ulam stability of linear differential operator with constant coefficients T.Miura;S.Miyajima;S.E.Takahasi
  13. Proc. Amer. Math. Soc. v.83 Compact weighted endomorphisms of C(X) H.Kamowitz
  14. Composition operators on function spaces R.K.Singh;J.S.Manhas

Cited by

  1. On the best constant in Hyers–Ulam stability of some positive linear operators vol.412, pp.1, 2014,
  2. Best constant in stability of some positive linear operators vol.90, pp.4, 2016,
  3. Hyers–Ulam stability with respect to gauges vol.453, pp.1, 2017,
  4. Stability of some positive linear operators on compact disk vol.35, pp.6, 2015,
  5. Hyers–Ulam stability of linear functional differential equations vol.426, pp.2, 2015,
  6. Essential norm of substitution vector-valued integral operator on L1(Σ) space vol.448, pp.2, 2017,
  7. The Fréchet functional equation with application to the stability of certain operators vol.164, pp.1, 2012,
  8. Hyers–Ulam Stability of Differential Operators on Reproducing Kernel Function Spaces vol.10, pp.4, 2016,
  9. On the stability of some positive linear operators from approximation theory vol.5, pp.2, 2015,
  10. Hyers-Ulam Stability of Differentiation Operator on Hilbert Spaces of Entire Functions vol.2014, 2014,
  11. On the stability of some classical operators from approximation theory vol.31, pp.3, 2013,
  12. Composition Operators on Cesàro Function Spaces vol.2014, 2014,
  13. Hyers-Ulam stability of delay differential equations of first order vol.289, pp.1, 2016,
  14. Hyers–Ulam stability of impulsive integral equations pp.2198-2759, 2018,