A Note on Operational Superselection from Restricted Observable Algebras in Split Hilbert Spaces

This record contains a short technical note on operational superselection induced by restricted observable algebras in a split Hilbert space H_tot = H_+ direct-sum H_-. Assuming the physically implementable observables for a given agent close in a *-subalgebra A_+ subset B(H_+) embedded as A -> A ⊕ 0, we show that all accessible expectation values depend only on the ++ block rho_++ of the global state; inter-sector coherences are operationally invisible. This induces an operational equivalence relation on global states with a canonical representative given by the block-dephasing channel D(rho) = Pi_+ rho Pi_+ + Pi_- rho Pi_-. A short Schrodinger-picture two-qubit illustration is included.