$k$-bitransitive and compound operators on Banach spaces

  • N. Bamerni University of Duhok, 38 Zakho str., 1006 Aj Duhok, Duhok, Iraq
  • A. Kilicman Universiti Putra Malaysia, Jalan Upm, 43400 Serdang, Selangor, Malaysia
Keywords: hypercyclic operators, diskcyclic operators, weakly mixing operators, direct sums
Published online: 2016-06-30

Abstract


In this this paper, we introduce new classes of operators in complex Banach spaces, which we call $k$-bitransitive operators and compound operators to study the direct sum of diskcyclic operators. We create a set of sufficient conditions for an operator to be $k$-bitransitive or compound. We give a relation between topologically mixing operators and compound operators. Also, we extend the Godefroy-Shapiro Criterion for topologically mixing operators to compound operators.
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How to Cite
(1)
Bamerni N., Kilicman A. $k$-Bitransitive and Compound Operators on Banach Spaces. Carpathian Math. Publ. 2016, 8 (1), 3-10.