Non-ergodic Banach spaces are near Hilbert

2016/11/16 by W. Cuellar-Carrera, Cuellar-Carrera, W.
Mathematics · #46B03 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B20 #Secondary 03E15 #math.FA #msc:03E15 #msc:46B03 #msc:46B20

paper · pdf · doi:10.48550/arxiv.1611.05500

arxiv created 2016/11/16 · arxiv updated 2016/11/18

Abstract

We prove that a non ergodic Banach space must be near Hilbert. In particular, ℓ_p (2<p<∞) is ergodic. This reinforces the conjecture that ℓ₂ is the only non ergodic Banach space. As an application of our criterion for ergodicity, we prove that there is no separable Banach space which is complementably universal for the class of all subspaces of ℓ_p, for 1≤ p <2. This solves a question left open by W. B. Johnson and A. Szankowski in 1976.

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