A note on James spaces and superstrictly singular operators

TL;DR

This paper demonstrates that the natural inclusion between James spaces is superstrictly singular for p<q, and shows that Read's operator without nontrivial invariant subspaces is also superstrictly singular, using an elementary lemma.

Contribution

It introduces a simple lemma to establish superstrictly singular properties of certain operators and inclusions in James spaces, extending understanding of their structure.

Findings

The inclusion J_p to J_q is superstrictly singular for p<q.

Read's operator without nontrivial invariant subspaces is superstrictly singular.

Elementary lemma effectively proves superstrictly singularity in these contexts.

Abstract

An elementary lemma is used in order to show that the natural inclusion $J_p\to J_q$ of James spaces is superstrictly singular for $p<q$. As a consequence, it is shown that an operator without nontrivial invariant subspaces constructed by Charles Read is superstrictly singular.