2020/01/30 by Gelu Popescu, Popescu, Gelu
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2001.11392
openalex publication_date 2020/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain a noncommutative multivariable analogue of Louhichi and Olofsson\ncharacterization of Toeplitz operators with harmonic symbols on the weighted\nBergman space Am( bf D), as well as Eschmeier and Langendorfer extension\nto the unit ball of bf Cn. All our results are proved in the more general\nsetting of noncommutative poly-hyperballs bf Dnm(H), bf n,m\∈ bf\nNk, and are used to characterize the bounded free k-pluriharmonic\nfunctions with operator coefficients on poly-hyperballs and to solve the\nassociated Dirichlet extension problem. In particular, the results hold for the\nreproducing kernel Hilbert space with kernel\n \n
kappa
bf m(z,w):=
prodi=1k
frac1(1-
bar zi wi)mi,
qquad\nz,w
in
bf Dk,\n\n where mi\≥ 1. This includes the Hardy space, the Bergman space, and the\nweighted Bergman space over the polydisk.\n