Brief Communications

Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 232-233

First online:

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

  • K. V. StorozhukAffiliated withSobolev institute of mathematics SB RAS, Novosibirsk State University Email author 

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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).

Key words

Kronecker set asymptotically finite-dimensional operator