Abstract
We consider some conditions for continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions of bounded type on $$\ell _1, L_\infty [0,1)$$, and $$L_\infty [0,\infty )\,{\cap }\, L_1[0,\infty )$$. We establish hypercyclicity of some special composition operators, namely of compositions with translations on algebras of symmetric analytic functions and some other algebras generated by countable sequences of homogeneous polynomials.
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