Hypercyclic Criterion for Tuples on Hilbert Spaces

Mezban Habibi Babadi¹

1) Mathematical Analysis Ph.D student, Payam Noor University.

IOI Code : XCZE-ECGFD
Publication : 3.rd International Congress of Science, Engineering and Technology - Hamburg(germanconf.com)
Abstract :
    The paper gives a survey of commutator tuples and infinity tuples of commutative bounded linear mappings on a Hilbert space, also we will investigate the properties of nuclear class of tuples and non-hypercyclic tuples. Let be an ordered Hilbert space and are commutative bounded linear operators on . If take . For , define . The tuple is called hypercyclic if there is a vector such that, the set is dense in . In this case, the vector is called a hypercyclic vector for and is called hypercyclic tuple, the tuple is hypercyclic if and only if it is topologically transitive. If is hypercyclic vector for and be non negative integers, then is hypercyclic vector for .

Keywords : hilbert space hypercyclic criterion hypercyclic tuple hypercyclic vector