On Linear Chaos in the Space of Convergent Sequences

The paper proves that naive extensions of weighted backward shifts to c are not hypercyclic (bounded and unbounded), constructs a bounded homeomorphic isomorphism J:c→c0(Z+), and via conjugacy builds bounded and unbounded chaotic operators on c with explicit spectra and iterate formulas. The candidate solution reproduces the same constructions and conclusions, differing mainly in proof style: it gives classical block-lacunary constructions for hypercyclicity and periodic points instead of invoking the paper’s sufficient condition for chaos, but all claims align with the paper’s results, including the non-hypercyclicity arguments, the conjugacy via J, the chaoticity and dense periodic points of the constructed operators, and the spectral statements for the bounded case and the full point spectrum for the unbounded case. See the paper’s abstract and main statements, including Proposition 4.1 and 4.2 (non-hypercyclicity on c), Lemma 5.1 (the isomorphism J), Theorem 5.1 (bounded chaotic Âw on c, spectrum), and Theorem 5.2 (unbounded chaotic Âw on c, powers and domains), together with the c0 results in Theorems 3.1 and 3.2 that are transferred by conjugacy .