Noah Schoem : Anti-Choice Axioms and the Dual of $\ell^\infty$

Posted by Noah Schoem , part of the Louise Hay Logic Seminar.

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Oct. 18, 2018, 4 p.m.

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427 SEO

Abstract

In most functional analysis courses, $\ell^1$ is often an example of a Banach space that is not reflexive; that is, $(\ell^1)^*$, the dual space of $\ell^1$, is $\ell^\infty$, but $(\ell^\infty)^*\supsetneq \ell^1$. However, this argument requires the Axiom of Choice. In fact, we will show that under a certain anti-choice axiom, that $(\ell^\infty)^*=\ell_1$.