, Volume 46, Issue 3, pp 232-233
Date: 14 Sep 2012

Isometries with dense windings of the torus in C(M)

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Abstract

Let C(M) be the space of all continuous functions on M⊂ ℂ. We consider the multiplication operator T: C(M) → C(M) defined by Tf(z) = zf(z) and the torus $$ O(M) = \left\{ {f:M \to \mathbb{C} \ntrianglelefteq \left\| f \right\| = \left\| {\frac{1} {f}} \right\| = 1} \right\} $$ . If M is a Kronecker set, then the T-orbits of the points of the torus ½O(M) are dense in ½O(M) and are ½-dense in the unit ball of C(M).

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 3, pp. 89–91, 2012
Original Russian Text Copyright © by K. V. Storozhuk
This work was supported by the program “Leading Scientific Schools,” grant no. NSh-6613.2010.1.