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Strong Convergence of Cesaro Means of Firmly Nonexpansive Iterates

Analysis · posed by 1975 · disproved

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Statement

Iterates of a firmly nonexpansive operator converge weakly but not strongly, by Genel and Lindenstrauss. Whether their Cesaro means converge strongly was open. They need not: an explicit curve gives a counterexample.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Heinz H. Bauschke and Tran Thanh Tung, using ChatGPT 5.5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The acknowledgement credits use of ChatGPT 5.5 as leading eventually to the realization of the explicit curve, which is the object the counterexample is built from.

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open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.