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arXiv · 2609.27061

Adjoints, Order and Spectral Moduli on $L^2(T)$

Mohamed Amine Ben Amor
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Abstract

We study adjoints of $R(T)$-linear, $T$-strongly bounded operators on the conditional space $L^2(T)$ 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.

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Mohamed Amine Ben Amor. 2026-09-22. Adjoints, Order and Spectral Moduli on $L^2(T)$. https://arxiv.org/abs/2609.27061

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