2020/05/30 by Eleftherios Kastis, S. C. Power, Kastis, Eleftherios +1
Mathematics · #47L35 #47L75 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2006.00307
openalex publication_date 2020/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The parabolic algebra Ap is the weakly closed algebra on L2(R) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions eiλx, λ≥ 0. This algebra is reflexive with an invariant subspace lattice, Lat Ap, which is naturally homeomorphic to the unit disc (Katavolos and Power, 1997). This identification is used here to classify strongly irreducible isometric representations of the partial Weyl commutation relations. The notion of a synthetic subspace lattice is extended from commutative to noncommutative lattices and it is shown that Lat Ap is nonsynthetic relative to the maximal abelian multiplication subalgebra of Ap. Also, operator algebras derived from isometric representations of Ap and from compact perturbations are defined and determined.