Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 303-01. Weak pure infiniteness and O-infinity absorption
Manuscript map · lines 8395–8404
OpenAI@2026-10-07#rem:oai-p-303-01
Authors: OpenAI. Family 303.
Title: Weak pure infiniteness and O-infinity absorption.
Abstract: We prove that every complex C∗-algebra in which each positive element is properly infinite is strongly purely infinite. This answers the ordinary-to-strong part of Kirchberg–Rørdam's comparison question. For exact algebras, we also prove that proper infiniteness of one fixed finite amplification of every positive element implies proper infiniteness of each positive element. Consequently, every separable nuclear algebra with this fixed-amplification property absorbs ${}mathcal O_{}infty$, without assumptions of unitality or simplicity.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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