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Supercyclic Subspaces
Author(s) -
MontesRodríguez Alfonso,
Salas Héctor N.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930300242x
Subject(s) - mathematics , linear subspace , scalar (mathematics) , bounded operator , orbit (dynamics) , operator (biology) , bounded function , banach space , pure mathematics , operator space , finite rank operator , discrete mathematics , mathematical analysis , geometry , biochemistry , chemistry , engineering , repressor , transcription factor , gene , aerospace engineering
A bounded operator T acting on a Banach space B is said to be supercyclic if there is a vector x ∈ B such that the projective orbit {λ T n x : n ⩾ 0 and λ ∈ C} is dense in B. Examples of supercyclic operators are hypercyclic operators, in which the orbit itself is dense without the help of scalar multiples. Supercyclic operators are, in turn, a special case of cyclic operators. An operator is called cyclic if the linear span of the orbit of some vector is dense in the underlying space. This survey describes some recent results on linear subspaces in which all elements, except the zero vector, are supercyclic for a given supercyclic operator. 2000 Mathematics Subject Classification 47A16.