Geodesic
Isometries with Dense Windings of the Torus in $C(M)$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 89-91.

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Let $C(M)$ be the space of all continuous functions on $M\subset\mathbb{C}$. We consider the multiplication operator $T\colon C(M)\to C(M)$ defined by $Tf(z)=zf(z)$ and the torus $O(M)=\{f:M\to\mathbb{C},\, \|f\|=\|\frac{1}{f}\|=1\}$. If $M$ is a Kronecker set, then the $T$-orbits of the points of the torus $\frac12 O(M)$ are dense in $\frac12 O(M)$ and are $\frac12$-dense in the unit ball of $C(M)$.
Keywords: Kronecker set, asymptotically finite-dimensional operator. 
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K. V. Storozhuk. Isometries with Dense Windings of the Torus in $C(M)$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 89-91. http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a7/

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