Some Representation Theorem for nonreflexive Banach space ultrapowers under the Continuum Hypothesis

TL;DR

Under the Continuum Hypothesis, the paper proves that nonreflexive Banach space ultrapowers are isometrically isomorphic to spaces of continuous functions on the Parovicenko space, aiding geometric and topological analysis.

Contribution

It establishes a representation theorem linking nonreflexive Banach space ultrapowers to continuous functions on the Parovicenko space under CH, a novel structural insight.

Findings

Ultrapowers are isometrically isomorphic to continuous functions on Parovicenko space.

The theorem facilitates analysis of geometry and topology of Banach space ultrapowers.

Provides a new tool for studying nonreflexive Banach spaces under CH.

Abstract

In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real-valued functions on the Parovicenko space. This Representation Theorem will be helpful in proving some facts from geometry and topology of nonreflexive Banach space ultrapowers.