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Noncommutative von Neumann-Riesz and von Neumann-Riesz-Lorch Mean Ergodic Theorems

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Contributed by K. MAHESH KRISHNA ↗

Version 1 / Nov 05, 2026 / CC BY 4.0

Abstract

We derive noncommutative von Neumann-Riesz and von Neumann-Riesz-Lorch mean ergodic theorems for adjointable contractions on a Hilbert C*-module. We crucially use a result obtained by Paschke [\textit{Trans. Amer. Math. Soc., 1973}]. We also note that the exact version of the noncommutative von Neumann–Riesz mean ergodic theorem fails.

Provenance statement

AI (GPT, Claude, Gemini) is used for the literature survey. Claude AI by Anthropic (free version) was used to obtain Example 2.7.

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Version history

  1. v1 · 7 pagesSubmitted by K. MAHESH KRISHNAInitial depositCurrentNov 04, 2026