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PreprintCC BY 4.0arXiv

Pointwise Ergodic Theorems Along Reiter Sequences on Locally Compact Groups

  • Panchugopal Bikram
  • Sudipta Kundu
  • Hariharan G
  • Diptesh Saha
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Abstract

Let G be a locally compact, second countable group admitting a Reiter sequence, and suppose that G acts on a von Neumann algebra ℳ equipped with a semifinite trace τ via trace-preserving automorphisms. In this paper, we prove a maximal inequality for ergodic averages along such Reiter sequences. Our approach relies on approximating the Reiter sequence by a linear combination of characteristic functions of Følner sequences using the layer-cake representation. Furthermore, we establish the bilateral almost uniform convergence of these ergodic averages. As an application, we deduce a non-commutative Wiener-Wintner type theorem along Reiter sequences.

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Cite

BibTeXRIS
BibTeX
@misc{bikram2026pointwise,
  title = {{Pointwise Ergodic Theorems Along Reiter Sequences on Locally Compact Groups}},
  author = {Panchugopal Bikram and Sudipta Kundu and Hariharan G and Diptesh Saha},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16580},
  eprint = {2610.16580},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16580},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Pointwise Ergodic Theorems Along Reiter Sequences on Locally Compact Groups
AU  - Panchugopal Bikram
AU  - Sudipta Kundu
AU  - Hariharan G
AU  - Diptesh Saha
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16580
UR  - https://arxiv.org/abs/2610.16580
AB  - Let G be a locally compact, second countable group admitting a Reiter sequence, and suppose that G acts on a von Neumann algebra ℳ equipped with a semifinite trace τ via trace-preserving automorphisms. In this paper, we prove a maximal inequality for ergodic averages along such Reiter sequences. Our approach relies on approximating the Reiter sequence by a linear combination of characteristic functions of Følner sequences using the layer-cake representation. Furthermore, we establish the bilateral almost uniform convergence of these ergodic averages. As an application, we deduce a non-commutative Wiener-Wintner type theorem along Reiter sequences.
ER  -