Notes about the structure of common supercyclic vectors |
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Authors: | Liang Zhang Ze-Hua Zhou |
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Institution: | 1. Department of Mathematics, Tianjin University, Tianjin 300072, PR China;2. Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China |
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Abstract: | In this paper, we give a sufficient condition for the existence of a common universal subspace for various countable families of universal sequences of linear operators. Besides, we show that if σp(T?)=∅, the unitary orbit of the supercyclic operator T contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology, and yet every nonzero vector in the linear span of the orbit of a given supercyclic vector is a common supercyclic vector for the entire path. |
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Keywords: | Path of supercyclic operators Unitary orbit Common supercyclic subspace |
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