Syndetic sequences and dynamics of operators
Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 537-545
Printed September 1, 2012
Hamid Rezaei
Yasouj University
Abstract : In the present paper, we show that a continuous linear operator $T$ on a Frechet space satisfies the Hypercyclic Criterion with respect to a syndetic sequence must satisfy the Kitai Criterion. On the other hand, an operator, hereditarily hypercyclic with respect to a syndetic sequence must be mixing. We also construct weighted shift operators satisfying the Hypercyclicity Criterion which do not satisfy the Kitai Criterion. In other words, hereditarily hypercyclic operators without being mixing.
Keywords : hypercyclic operator, hereditarily criterion, mixing operator
MSC numbers : Primary 47A16; Secondary 47B38
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