# The Schreier Space Does Not Have the Uniform $\lambda$-property

## TL;DR

This paper demonstrates that the Schreier space and its dual lack the uniform λ-property, clarifying a geometric aspect of these Banach spaces and answering a question posed in the late 1980s.

## Contribution

It proves that the Schreier space and its dual do not possess the uniform λ-property, resolving an open question from prior research.

## Key findings

- Schreier space does not have the uniform λ-property.
- The dual of Schreier space also lacks the uniform λ-property.
- Clarifies geometric properties of Schreier space in Banach space theory.

## Abstract

The $\lambda$-property and the uniform $\lambda$-property were first introduced by R. Aron and R. Lohman in 1987 as geometric properties of Banach spaces. In 1989, Th. Shura and D. Trautman showed that the Schreier space possesses the $\lambda$-property and asked if it has the uniform $\lambda$-property. In this paper, we show that Schreier space does not have the uniform $\lambda$-property. Furthermore, we show that the dual of the Schreier space does not have the uniform $\lambda$-property.