Small operator ideals on the Schlumprecht and Schreier spaces

Abstract

We present a method of building operators on a Banach space $X$ that generate distinct operator ideals in the algebra $\mathcal{B}(X)$ of bounded linear operators on $X$. We show that there are exactly $2^{\mathfrak{c}}$ distinct small closed operator ideals on the Schlumprecht space and there is a chain of cardinality $\mathfrak{c}$ of small closed operator ideals on any Schreier space of finite order.

Strenghtened results on Schreier spaces, redaction corrections