The parabolic algebra on Banach spaces

2016/03/10 by Eleftherios Kastis, Kastis, Eleftherios
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1603.03426

openalex publication_date 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The parabolic algebra was introduced by Katavolos and Power, in 1997, as the operator algebra acting on L²(R) that is weakly generated by the translation and multiplication semigroups. In particular, they proved that this algebra is reflexive and is equal to the Fourier binest algebra, that is, to the algebra of operators that leave invariant the subspaces of the Volterra nest and its analytic counterpart. We prove that a similar result holds for the corresponding algebras acting on L^p(R), where 1

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