Norm closed ideals in the algebra of bounded linear operators on Orlicz sequence spaces

Abstract

For each $1<p<\infty$, we consider a class of $p$-regular Orlicz sequence spaces $\ell _M$ that are “close” to $\ell _p$ and study the structure of the norm closed ideals in the algebra of bounded linear operators on such spaces. We show that the unique maximal ideal in $L(\ell _M)$ is the set of all $\ell _M$ strictly singular operators and the immediate successor of the ideal of compact operators in $L(\ell _M)$ is the closed ideal generated by the formal identity from $\ell _M$ into $\ell _p$.