Open AccessHypercyclictty and Countable Hypercyclicity for Adjoint of Operators
Author(s) -
Baghdad Science Journal
Publication year - 2010
Publication title -
mağallaẗ baġdād li-l-ʿulūm
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.167
H-Index - 6
eISSN - 2411-7986
pISSN - 2078-8665
DOI - 10.21123/bsj.7.1.191-199
Subject(s) - mathematics , separable space , countable set , bounded operator , bounded function , subspace topology , hilbert space , banach space , operator (biology) , pure mathematics , spectrum (functional analysis) , discrete mathematics , mathematical analysis , chemistry , biochemistry , physics , repressor , quantum mechanics , transcription factor , gene
Let be an infinite dimensional separable complex Hilbert space and let , where is the Banach algebra of all bounded linear operators on . In this paper we prove the following results.If is a operator, then 1. is a hypercyclic operator if and only if D and for every hyperinvariant subspace of .2. If is a pure, then is a countably hypercyclic operator if and only if and for every hyperinvariant subspace of .3. has a bounded set with dense orbit if and only if for every hyperinvariant subspace of , .