Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers\n are primary

2011/07/08 by Piotr Wilzcek, Wilzcek, Piotr
Computer Science · Mathematics · #46B08 #46B20 #46B25 #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Logic (math.LO) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1107.1692

openalex publication_date 2011/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note a large class of primary Banach spaces is characterized. Namely,\nit will be demonstrated that under the Continuum Hypothesis the ultrapower of\nany infinite dimensional nonsuperreflexive Banach space is always primary.\nConsequently, any infinite dimensional nonsuperreflexive Banach space can be\nisometrically embedded into its primary ultrapowers.\n

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