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A weighted bilateral shift with cyclic square is supercyclic
Author(s) -
Shkarin Stanislav
Publication year - 2007
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/blms/bdm085
Subject(s) - mathematics , bounded function , square (algebra) , combinatorics , pure mathematics , mathematical analysis , geometry
It is shown, for a bounded weighted bilateral shift T acting on ℓ p (ℤ), and for 1⩽ p ⩽2, that supercyclicity of T , weak supercyclicity of T , cyclicity of T ⊕ T and cyclicity of T 2 are equivalent. A new sufficient condition for cyclicity of a weighted bilateral shift is proved, which implies, in particular, that any compact weighted bilateral shift is cyclic.