Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2003; 40(4): 583-591

Printed December 1, 2003

Copyright © The Korean Mathematical Society.

Essential Norms and stability constants of weighted composition operators on $C(X)$

Hiroyuki Takagi, Takeshi Miura, and Sin-Ei Takahasi

Shinshu University, Yamagata University, Yamagata University

Abstract

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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 $\varphi ( \{ x \in X : |u(x)| \geq r \} )$ ($r > 0$).

Keywords: weighted composition operator, essential norm, Hyers-Ulam stability, closed range

MSC numbers: 47B33, 34K20

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