Szlenk Index, Upper Estimates, and Embedding in Banach Spaces
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We investigate the relationship between two notions, one which refers to a coordinate system and one which does not, of asymptotic domination by subsequences of a fixed basis. We use this relationship to prove the existence of a universal space with a coordinate system satisfying this asymptotic domination condition. Last, we relate this asymptotic domination notion to the Szlenk index and prove a result concerning the existence of a universal space for classes determined by Szlenk index. Each of these results also has a corresponding result for reflexive spaces.
Causey, Ryan Michael (2014). Szlenk Index, Upper Estimates, and Embedding in Banach Spaces. Doctoral dissertation, Texas A & M University. Available electronically from