Li–Yorke chaos for composition operators on Orlicz spaces

In this paper we characterize Li–Yorke chaotic composition operators on Orlicz spaces. Indeed, some necessary and sufficient conditions are provided for Li–Yorke chaotic composition operator <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>C</m:mi> <m:mi>φ</m:mi> </m:msub> </m:math> {Cφ} on the Orlicz space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>L</m:mi> <m:mi mathvariant="normal">Φ</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>μ</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {LΦ(μ)} . In some cases we have equivalent conditions for composition operators on Orlicz spaces to be Li–Yorke chaotic. The results of this paper extend similar results in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mi>p</m:mi> </m:msup> </m:math> {Lᵖ} -spaces.