On hypercyclicity and linear chaos in a nonclassical sequence space and beyond
Abstract
We analyze the hypercyclicity, chaoticity, and spectral structure of (bounded and unbounded) weighted backward shifts in a nonclassical sequence space, which the space l1 of summable sequences is both isometrically isomorphic to and continuously and densely embedded into. Based on the weighted backward shifts, we further construct new bounded and unbounded linear hypercyclic and chaotic operators both in the nonclassical sequence space and the classical space l1, including those that are hypercyclic but not chaotic.
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