Closed ideals of operators on the Baernstein and Schreier spaces

We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces B-p for 1 <= p < infinity and the p- convexified Schreier spaces S p for 1 p < infinity. Our main conclusion is that there are 2(c )many closed ideals that lie between the ideals of compact and strictly singular operators on each of these spaces, and also 2(c ) many closed ideals that contain projections of infinite rank. Counterparts of results of Gasparis and Leung using a numerical index to distinguish the isomorphism types of subspaces spanned by subsequences of the unit vector basis for the classical Schreier space S 1 and its higher-order variants play a key role in the proofs, as does the Johnson-Schechtman technique for constructing 2c many closed ideals of operators on a Banach space. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).