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arXiv · 2608.08278

The Borel complexity of non-Archimedean operator ranges

Martino Lupini
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Abstract

We completely classify the possible complexity classes of non-closed operator ranges on separable Banach spaces over a Polish non-Archimedean non-trivially valued field. These are precisely $\boldsymbol{\Pi }_{1+\lambda +n+2}^{0}$ for a countable ordinal $\lambda $ that is either zero or a limit ordinal, and a finite ordinal $n$. Considering Fr\'echet spaces produces the additional complexity classes $\boldsymbol{\Pi }_{\lambda }^{0}$ for a countable limit ordinal $\lambda $.

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Martino Lupini. 2026-08-08. The Borel complexity of non-Archimedean operator ranges. https://arxiv.org/abs/2608.08278

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