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PreprintCC BY-NC-ND 4.0arXiv

Adjoints, Order and Spectral Moduli on L2(T)

  • Mohamed Amine Ben Amor
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Abstract

We study adjoints of R(T)-linear, T-strongly bounded operators on the conditional space L2(T) and the interaction between its Hilbert-type geometry and its Riesz-space order. This produces two natural operator moduli: the Riesz--Kantorovich order modulus and the spectral modulus (S*S)1/2. After isolating the T-regular operators, we show that they form a Dedekind-complete order ideal in the natural lattice of order-bounded R(T)-module homomorphisms. On this operator lattice the order operations remain T-strongly bounded and the adjoint is an order automorphism. We then compare the two moduli and explain why they may differ.

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Cite

BibTeXRIS
BibTeX
@misc{amor2026adjoints,
  title = {{Adjoints, Order and Spectral Moduli on $L^2(T)$}},
  author = {Mohamed Amine Ben Amor},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27061},
  eprint = {2609.27061},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27061},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Adjoints, Order and Spectral Moduli on L^2(T)
AU  - Mohamed Amine Ben Amor
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.27061
UR  - https://arxiv.org/abs/2609.27061
AB  - We study adjoints of R(T)-linear, T-strongly bounded operators on the conditional space L^2(T) and the interaction between its Hilbert-type geometry and its Riesz-space order. This produces two natural operator moduli: the Riesz--Kantorovich order modulus and the spectral modulus (S^*S)^1/2. After isolating the T-regular operators, we show that they form a Dedekind-complete order ideal in the natural lattice of order-bounded R(T)-module homomorphisms. On this operator lattice the order operations remain T-strongly bounded and the adjoint is an order automorphism. We then compare the two moduli and explain why they may differ.
ER  -