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By strengthening one of the hypotheses of a well-known sufficient conditionfor the hypercyclicity of linear operators in Banach spaces, we arrive at asufficient condition for linear chaos and reveal consequences of the latter forinverses, powers, multiples, and spectral properties. Extending the results,familiar for bounded linear operators, we also show that the hypercyclicity ofunbounded linear operators subject to the sufficient condition forhypercyclicity is inherited by their bounded inverses, powers, and unimodularmultiples and that necessary conditions for linear hypercyclicity stretch tothe unbounded case.

On sufficient and necessary conditions for linear hypercyclicity and chaos