Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers are primary

TL;DR

Under the Continuum Hypothesis, the paper proves that ultrapowers of all infinite dimensional nonsuperreflexive Banach spaces are primary, and such spaces can be embedded into these ultrapowers, expanding understanding of Banach space structure.

Contribution

It characterizes a large class of primary Banach spaces as ultrapowers of nonsuperreflexive spaces under the Continuum Hypothesis, revealing new structural properties.

Findings

Ultrapowers of nonsuperreflexive Banach spaces are primary under CH

Any such Banach space embeds isometrically into its ultrapower

Provides a new class of primary Banach spaces

Abstract

In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary. Consequently, any infinite dimensional nonsuperreflexive Banach space can be isometrically embedded into its primary ultrapowers.