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Banach Gelfand Triples with Kernel Theorems via Equivalence Bimodules

  • Dimitri Bytchenkoff
  • Arvin Lamando
  • Franz Luef
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Abstract

Hilbert C*-modules whose coefficient C*-algebra is equipped with a finite faithful trace generate Banach Gelfand triples. This provides a natural setting for the interpretation of Hilbert C*-modules as function spaces. In particular, when the modules are finitely generated and projective, their external tensor products interact well with projective tensor products. This allowed us to derive abstract kernel theorems for Hilbert C*-modules. As an application, we apply our results to Heisenberg modules and obtain new kernel theorems for time-frequency analysis.

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Cite

BibTeXRIS
BibTeX
@misc{bytchenkoff2026banach,
  title = {{Banach Gelfand Triples with Kernel Theorems via Equivalence Bimodules}},
  author = {Dimitri Bytchenkoff and Arvin Lamando and Franz Luef},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.37780},
  eprint = {2609.37780},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37780},
}
RIS
TY  - UNPB
TI  - Banach Gelfand Triples with Kernel Theorems via Equivalence Bimodules
AU  - Dimitri Bytchenkoff
AU  - Arvin Lamando
AU  - Franz Luef
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.37780
UR  - https://arxiv.org/abs/2609.37780
AB  - Hilbert C*-modules whose coefficient C*-algebra is equipped with a finite faithful trace generate Banach Gelfand triples. This provides a natural setting for the interpretation of Hilbert C*-modules as function spaces. In particular, when the modules are finitely generated and projective, their external tensor products interact well with projective tensor products. This allowed us to derive abstract kernel theorems for Hilbert C*-modules. As an application, we apply our results to Heisenberg modules and obtain new kernel theorems for time-frequency analysis.
ER  -