Submitted:
16 November 2020
Posted:
18 November 2020
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Abstract
In this paper we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms which show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator which is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclisity of composition operators.
Keywords:
topologically transitive operator
; hypercyclic operators
; function space
; analytic functions on Banach spaces
; symmetric polynomials on Banach spaces
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