Quotients of Banach spaces and surjectively universal spaces

TL;DR

This paper characterizes classes of separable Banach spaces for which there exists a universal quotient space that does not contain ree_1, providing insights into the structure of Banach space quotients.

Contribution

It introduces a characterization of classes of Banach spaces with a universal quotient space not containing ree_1, advancing understanding of Banach space quotients.

Findings

Identifies conditions for classes of Banach spaces to have a universal quotient

Constructs examples of such universal quotient spaces

Provides criteria for the absence of ree_1 in these spaces

Abstract

We characterize those classes $\mathcal{C}$ of separable Banach spaces for which there exists a separable Banach space $Y$ not containing $\ell_1$ and such that every space in the class $\mathcal{C}$ is a quotient of $Y$.