Separately Radial and Radial Toeplitz Operators on the Unit Ball and\n Representation Theory

2015/09/23 by Raúl Quiroga-Barranco, Quiroga-Barranco, Raul
Mathematics · #22E46 #32A36 #32M15 #47B35 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1509.07063

openalex publication_date 2015/09/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study Toeplitz operators with separately radial and radial symbols on the\nweighted Bergman spaces on the unit ball. The unitary equivalence of such\noperators with multiplication operators on \ℓ² spaces was previously\nobtained by analytic methods elsewhere (see the references). We prove that the\nsame constructions can be performed with a purely representation theoretic\napproach to obtain the same conclusions and formulas. However, our method is\nshorter, more elementary and more elucidating.\n

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