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Funktsional. Anal. i Prilozhen., 2012, Volume 46, Issue 3, Pages 89–91 (Mi faa3072)  

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

DOI: https://doi.org/10.4213/faa3072

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English version:
Functional Analysis and Its Applications, 2012, 46:3, 232–233

Bibliographic databases:

UDC: 517.983.23
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

Citation in format AMSBIB
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