The Lambda Property and Isometries for Higher Order Schreier Spaces (thesis)
Chu, Hung Viet
Washington and Lee University -- Honors in Mathematics
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Hung Viet Chu is a member of the Class of 2019 of Washington and Lee University.Thesis; [FULL-TEXT FREELY AVAILABLE ONLINE]For each n in N, let Sn be the Schreier set of order n and XSn be the corresponding Schreier space of order n. In their 1989 paper "The lambda-property in Schreier space S and the Lorentz space d(a, 1)," Th. Shura and D. Trautman proved that the Schreier space of order 1 has the lambda-property. This thesis extends the theorem by proving the lambda-property for the Schreier spaces of any order and the uniform lambda-property (stronger than the lambda-property) for the p-convexification of these spaces. Furthermore, using what we know about extreme points of the unit balls, we are able to characterize all surjective linear isometries of these spaces.