Continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions on Banach spaces (Q1987703)

Some conditions for continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions of bounded type on different Banach spaces are presented in this paper. In Section~2, algebras generated by countable sequences of homogenous polynomials and composition operators on these algebras are studied. Continuity and hypercyclicity of such operators, especially for algebras of symmetric analytic functions, are investigated in Section~3. The authors establish hypercyclicity of some composition operators with translations on algebras of symmetric analytic functions and some other algebras. They also prove the hypercyclicity of related operators of differentiation.