On linear operators having supercyclic vectors

Gerd Herzog

Studia Mathematica (1992)

  • Volume: 103, Issue: 3, page 295-298
  • ISSN: 0039-3223

Abstract

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We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.

How to cite

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Herzog, Gerd. "On linear operators having supercyclic vectors." Studia Mathematica 103.3 (1992): 295-298. <http://eudml.org/doc/215953>.

@article{Herzog1992,
abstract = {We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.},
author = {Herzog, Gerd},
journal = {Studia Mathematica},
keywords = {supercyclic vectors},
language = {eng},
number = {3},
pages = {295-298},
title = {On linear operators having supercyclic vectors},
url = {http://eudml.org/doc/215953},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Herzog, Gerd
TI - On linear operators having supercyclic vectors
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 3
SP - 295
EP - 298
AB - We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.
LA - eng
KW - supercyclic vectors
UR - http://eudml.org/doc/215953
ER -

References

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  1. [1] B. Beauzamy, An operator in a separable Hilbert space with many hypercyclic vectors, Studia Math. 87 (1987), 71-78. Zbl0647.46024
  2. [2] B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North-Holland, 1988. Zbl0663.47002
  3. [3] P. S. Bourdon and J. H. Shapiro, Cyclic composition operators in H 2 , in: Proc. Sympos. Pure Math. 51, Amer. Math. Soc., 1990, 43-53. 
  4. [4] K.-G. Große-Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Gieß en 176 (1987). 
  5. [5] D. A. Herrero and Z.-Y. Wang, Compact perturbations of hypercyclic and supercyclic operators, Indiana Univ. Math. J. 39 (1990), 819-829. Zbl0724.47009
  6. [6] G. Herzog und R. Lemmert, Endomorphismen mit dichten Bahnen, preprint. 
  7. [7] G. Pólya und G. Szegő, Aufgaben und Lehrsätze aus der Analysis, Band I, Springer, 1964. Zbl0122.29704
  8. [8] S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17-22. Zbl0174.44203

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