On the three-space property for subprojective and superprojective Banach spaces

TL;DR

This paper introduces subprojective and superprojective operators, demonstrating a variation of the three-space property for these spaces and showing certain classical spaces possess both properties.

Contribution

It defines subprojective and superprojective operators and proves a new three-space property variation for these classes of Banach spaces.

Findings

Some classical spaces are both subprojective and superprojective.

A variation of the three-space property is established for these spaces.

The notions of subprojective and superprojective operators are introduced and analyzed.

Abstract

We introduce the notion of subprojective and superprojective operators and we use them to prove a variation of the three-space property for subprojective and superprojective spaces. As an application, we show that some spaces considered by Johnson and Lindenstrauss are both subprojective and superprojective.