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PreprintCC BY 4.0arXiv

A note on the stability of Arens products under small perturbations of multiplication

  • Deepika Rajoriya
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Abstract

In this short note, we study the small perturbations of multiplication structure of a Banach algebra π’œ, and its impact on the two Arens products on the bidual π’œ**. We show that the property of being \say{Arens irregular} is stable under sufficiently small perturbation in the multiplication structure of a Banach algebra. Further we show that for any Banach function algebra which is equivalent to a uniform algebra, the Arens regularity is stable under small perturbation on the multiplication structure of the original Banach function algebra.

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Cite

BibTeXRIS
BibTeX
@misc{rajoriya2026note,
  title = {{A note on the stability of Arens products under small perturbations of multiplication}},
  author = {Deepika Rajoriya},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11379},
  eprint = {2609.11379},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11379},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A note on the stability of Arens products under small perturbations of multiplication
AU  - Deepika Rajoriya
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11379
UR  - https://arxiv.org/abs/2609.11379
AB  - In this short note, we study the small perturbations of multiplication structure of a Banach algebra π’œ, and its impact on the two Arens products on the bidual π’œ^**. We show that the property of being \say{Arens irregular} is stable under sufficiently small perturbation in the multiplication structure of a Banach algebra. Further we show that for any Banach function algebra which is equivalent to a uniform algebra, the Arens regularity is stable under small perturbation on the multiplication structure of the original Banach function algebra.
ER  -