Abstract

In this paper, we show that every complex Banach space X with dimension at least 2 supports a numerically hypercyclic d-homogeneous polynomial P for every $${d\in \mathbb{N}}$$ . Moreover, if X is infinite-dimensional, then one can find hypercyclic non-homogeneous polynomials of arbitrary degree which are at the same time numerically hypercyclic. We prove that weighted shift polynomials cannot be numerically hypercyclic neither on c 0 nor on l p for 1 ≤ p < ∞. In contrast, we characterize numerically hypercyclic weighted shift polynomials on l∞.

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