k-bitransitive and compound operators on Banach spaces

TL;DR

This paper introduces new classes of operators called k-bitransitive and compound operators in complex Banach spaces, exploring their properties, relationships, and extending existing criteria for topologically mixing operators.

Contribution

It defines and analyzes k-bitransitive and compound operators, providing sufficient conditions and extending the Godefroy-Shapiro Criterion to these classes.

Findings

Established conditions for k-bitransitivity and compound operators.

Linked topologically mixing operators with compound operators.

Extended the Godefroy-Shapiro Criterion to the context of compound operators.

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 k-bitransitivity and compound. We show the relation between topologically mixing operators and compound operators. Also, we extend the Godefroy-Shapiro Criterion for topologically mixing operators to compound operators.