Fixed points and orbits of non-convolution operators
F León-Saavedra, P Romero-de la Rosa - Fixed Point Theory and …, 2014 - Springer
Fixed Point Theory and Applications, 2014•Springer
A continuous linear operator T on a Fréchet space F is hypercyclic if there exists a vector f∈
F (which is called hypercyclic for T) such that the orbit {T nf: n∈ N} is dense in F. A subset M
of a vector space F is spaceable if M∪{0} contains an infinite-dimensional closed vector
space. In this paper note we study the orbits of the operators T λ, bf= f′(λ z+ b)(λ, b∈ C)
defined on the space of entire functions and introduced by Aron and Markose (J. Korean
Math. Soc. 41 (1): 65-76, 2004). We complete the results in Aron and Markose (J. Korean …
F (which is called hypercyclic for T) such that the orbit {T nf: n∈ N} is dense in F. A subset M
of a vector space F is spaceable if M∪{0} contains an infinite-dimensional closed vector
space. In this paper note we study the orbits of the operators T λ, bf= f′(λ z+ b)(λ, b∈ C)
defined on the space of entire functions and introduced by Aron and Markose (J. Korean
Math. Soc. 41 (1): 65-76, 2004). We complete the results in Aron and Markose (J. Korean …
Abstract
A continuous linear operator T on a Fréchet space F is hypercyclic if there exists a vector (which is called hypercyclic for T) such that the orbit is dense in F. A subset M of a vector space F is spaceable if contains an infinite-dimensional closed vector space. In this paper note we study the orbits of the operators () defined on the space of entire functions and introduced by Aron and Markose (J. Korean Math. Soc. 41(1):65-76, 2004). We complete the results in Aron and Markose (J. Korean Math. Soc. 41(1):65-76, 2004), characterizing when is hypercyclic on . We characterize also when the set of hypercyclic vectors for is spaceable. The fixed point of the map (in the case ) plays a central role in the proofs.
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