Skip to content
DraconiticResearch
Search Sources API
184,937 studies31 sourcesUpdated 8 min ago
PreprintarXiv licencearXiv

A Banach--Stone-like Theorem for Slowly Oscillating Functions

  • Yutaka Iwamoto
Open at sourcePDFDOICite

Abstract

We prove that every lattice isomorphism between the lattices of slowly oscillating real-valued functions on proper metric spaces induces a coarse homeomorphism. This yields a Banach--Stone-like theorem for slowly oscillating functions, as well as a representation theorem for linear lattice isomorphisms between these function lattices. Both theorems were previously established by the author under the assumption of chain-connectedness. The present paper establishes both results for arbitrary proper metric spaces.

Related

  1. Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs
    Rémi Buffe, Alessandro Duca, Hugo Parada
    HALPreprintCC BY 4.0Full textAnalysis & PDEsOptimisation & controlHALarXiv
  2. Invariant means, coset correct means and the Hahn-Banach Theorem
    Armando Martino, Motiejus Valiunas
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  3. Spectral theorem for compact self-adjoint operators on smooth Banach spaces
    Mohammed Shameem
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. A Hartman-Grobman theorem on Banach bundles
    Benjamin Rogoll, Stefan Siegmund
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  5. Angles, orthogonality, and Pythagorean theorem in Banach spaces with two related applications
    Antonio Cicone, Stefano Serra-Capizzano, Giacomo Tento +1
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{iwamoto2026banachstonelike,
  title = {{A Banach--Stone-like Theorem for Slowly Oscillating Functions}},
  author = {Yutaka Iwamoto},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01629},
  eprint = {2611.01629},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01629},
}
RIS
TY  - UNPB
TI  - A Banach--Stone-like Theorem for Slowly Oscillating Functions
AU  - Yutaka Iwamoto
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01629
UR  - https://arxiv.org/abs/2611.01629
AB  - We prove that every lattice isomorphism between the lattices of slowly oscillating real-valued functions on proper metric spaces induces a coarse homeomorphism. This yields a Banach--Stone-like theorem for slowly oscillating functions, as well as a representation theorem for linear lattice isomorphisms between these function lattices. Both theorems were previously established by the author under the assumption of chain-connectedness. The present paper establishes both results for arbitrary proper metric spaces.
ER  -