ESSENTIAL NORMS AND STABILITY CONSTANTS OF WEIGHTED COMPOSITION OPERATORS ON C(X)

Title & Authors
ESSENTIAL NORMS AND STABILITY CONSTANTS OF WEIGHTED COMPOSITION OPERATORS ON C(X)
Takagi, Hiroyuki; Miura, Takeshi; Takahasi, Sin-Ei;

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