Abstract.
An operator on a separable, infinite dimensional Banach space satisfies the Hypercyclicity Criterion if and only if the associated left multiplication operator is hypercyclic; see [14], [16], [29]. By examining paths of operators where each operator along the path satisfies the criterion, we provide necessary and sufficient conditions for a path of left multiplication operators to have an SOT-dense set of common hypercyclic vectors. As a corollary, we establish a natural sufficient condition for a path of operators to have a common hypercyclic subspace.
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Sanders, R. Common Hypercyclic Vectors and the Hypercyclicity Criterion. Integr. equ. oper. theory 65, 131–149 (2009). https://doi.org/10.1007/s00020-009-1711-0
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DOI: https://doi.org/10.1007/s00020-009-1711-0