Assume that X is a Banach space such that its Szlenk index Sz X is less than or equal to the first infinite ordinal ω. We prove that X can be renormed in such a way that X with the resultant norm satisfies R X < 2, where R · is the Garcı́a-Falset coefficient. This leads us to prove that if X is a Banach space which can be continuously embedded in a Banach space Y with Sz Y ≤ ω, then, X can be re...
