Small operator ideals on the Schlumprecht and Schreier spaces

2020/08/27 by Manoussakis, Antonis, Pelczar-Barwacz, Anna
#46B15 #46B45 #46H10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2008.12362

Abstract

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

Related

• Closed ideals of operators on the Baernstein and Schreier spaces
• Operator Ideals arising from Generating Sequences
• Closed ideals of operators on the Tsirelson and Schreier spaces
• Classifying the closed ideals of bounded operators on two families of\n non-separable classical Banach spaces
• Banach spaces for which the space of operators has 2^{\mathfrak c} closed ideals