Continuous logic and embeddings of Lebesgue spaces

2018/05/29 by McNicholl, Timothy H.
#03C99 #46B04 #46B42 #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · doi:10.48550/arxiv.1805.11561

Abstract

We use the compactness theorem of continuous logic to give a new proof that L^r([0,1]; ℝ) isometrically embeds into L^p([0,1]; ℝ) whenever 1 ≤ p ≤ r ≤ 2. We will also give a proof for the complex case. This will involve a new characterization of complex L^p spaces based on Banach lattices.

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