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Zbl 1252.47027
Kamowitz, H.; Singh, R.K.; Wortman, D.
Compact substitution operators on weighted spaces of continuous functions.
(English)
[J] Ann. Funct. Anal. AFA 1, No. 2, 7-11, electronic only (2010). ISSN 2008-8752/e

The authors show that in the weighted setting the constants are the only symbols which define compact substitution operators $C_\phi(f)= f\circ \phi$ for $\phi:T\to T$ acting on spaces of continuous functions $CV_b(T)$ and $CV_0(T)$, defined on connected and completely regular Haussdorff spaces $T$, by the conditions $\sup_{t\in T}v(t)|f(t)|<\infty$ or $\lim_{t\to \infty}v(t)|f(t)|=0$ for any $v\in V$, respectively, where the weights system $V$ consists of families of upper-semicontinuous functions $v:T\to \mathbb R^+$ satisfying that $\lambda v\in V$ for any $v\in V$, for any couple $(u,v)\in V\times V$ there exists $w\in V$ with $u\le w$ and $v\le w$, and for any $t\in T$ there exists $v_t\in V$ with $v_t(t)>0$.
[Oscar Blasco (Valencia)]
MSC 2000:
*47B33 Composition operators
46J99 Commutative Banach algebras and commutative topological algebras
47B38 Operators on function spaces

Keywords: substitution operators; weighted spaces of continuous functions; system of weights

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