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ZHAO Xian-feng, SHU Yong-lu, ZHOU Yun-hua. Subspace-supercyclicity and common subspace-supercyclic vectors[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 106-112, 120.
Citation: ZHAO Xian-feng, SHU Yong-lu, ZHOU Yun-hua. Subspace-supercyclicity and common subspace-supercyclic vectors[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 106-112, 120.

Subspace-supercyclicity and common subspace-supercyclic vectors

  • Received Date: 2011-04-01
  • Rev Recd Date: 2011-07-01
  • Publish Date: 2012-01-25
  • A bounded linear operator $T$ on Banach space is subspace-supercyclic for a nonzero subspace $M$ if there exists a vector whose projective orbit intersects the subspace $M$ in a relatively dense set. We constructed examples to show that subspace-supercyclic is not a strictly infinite dimensional phenomenon, and that some subspace-supercyclic operators are not supercyclic. We provided a subspace-supercyclicity criterion and offered two necessary and sufficient conditions for a path of bounded linear operators to have a dense $G_\delta$ set of common subspace-hypercyclic vectors and common subspace-supercyclic vectors.
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