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In the collection "Aspects of Positivity in Functional Analysis. Proceedings of the Conference held on the Occasion of H.H. Schaefer's 60th Birthday", there is a contribution by Denes Petz titled "Almost uniform convergence on the predual of a von Neumann algebra and an ergodic theorem". However, for the key part of the proof of his noncommutative maximal inequality, he refers to a 1985 preprint titled "An individual ergodic theorem in the predual of a von Neumann algebra" by himself. I could not find an article with this title or anything close that could match.

My question: Have the contents of this preprint been published or, if not, is the preprint still available somewhere?

There is a reference to this result, still as a preprint, in a 1992 paper by Bartoszewicz with the title "On Almost Uniform Convergence of Some Sequences of States on Infinite Tensor Products of Von Neumann Algebras". So it seems like there was still no published version at this time.

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  • $\begingroup$ Petz cites it as "Preprint, Tübingen 1985". I didn't find anything in the University of Tübingen online library catalog, but maybe it's still hiding in some archive there. $\endgroup$ Commented Jun 18 at 3:03

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I could not locate the preprint. Here is what I got:

  • At the time of writing, Petz was a Humboldt fellow in the functional analysis group of Rainer Nagel at Tübingen. I looked through Nagel's archive of Petz's preprints and articles from this time, but it did not contain the preprint I was looking for (or another article that contains this result).
  • A colleague at Renyi asked the person who had cataloged Dénes Petz's preprints after his death, but this particular one wasn't included in this collection either.
  • Quanhua Xu, one of the leading experts in noncommutative ergodic theory, told me that he was unaware of this preprint and in fact considers the claimed result an open question.
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