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Brief communications
Isometries with Dense Windings of the Torus in $C(M)$
K. V. Storozhukab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
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.
Received: 18.10.2010
Citation:
K. V. Storozhuk, “Isometries with Dense Windings of the Torus in $C(M)$”, Funktsional. Anal. i Prilozhen., 46:3 (2012), 89–91; Funct. Anal. Appl., 46:3 (2012), 232–233
Linking options:
https://www.mathnet.ru/eng/faa3072https://doi.org/10.4213/faa3072 https://www.mathnet.ru/eng/faa/v46/i3/p89
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Abstract page: | 345 | Full-text PDF : | 179 | References: | 50 | First page: | 13 |
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