2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69587The L2-norm closure of the algebra of all zero-order classical (or polyhomogeneous) pseudodifferential operators on a closed manifold $X$ is proven not to contain Hörmander's class $Ψ^0(X)$. A set of generators (for that closed algebra) smaller than all zero-order classical pseudos is also described.Operator AlgebrasAnalysis of PDEs35S05;58J40;47G30text