Tingley's problem for Schreier spaces and their $p$-convexifications

TL;DR

This paper characterizes the surjective isometries of the unit sphere in real Schreier spaces and their p-convexifications, providing a positive answer to a special case of Tingley's problem for these spaces.

Contribution

It offers a complete description of sphere isometries in Schreier spaces and their p-convexifications, advancing understanding of Tingley's problem in these contexts.

Findings

Surjective isometries of the unit sphere are fully described.

Positive solution to a special case of Tingley's problem.

Extension of isometries to linear isometries established.

Abstract

We describe the surjective isometries of the unit sphere of real Schreier spaces of all orders and their $p$-convexifications, for $1 < p < \infty$. This description allows us to provide for those spaces a positive answer to a special case of Tingley's problem, which asks whether every surjective isometry of the unit sphere of a real Banach space can be extended to a linear isometry of the entire space.