The Schreier Space Does Not Have the Uniform $λ$-property

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.