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- W2938988892 abstract "In the present paper, we construct commutative algebras generated by Toeplitz operators on the Segal–Bargmann space Hs2(Cn) and on the true-k-Fock spaces. Analogous to the commutative Banach algebras constructed by N. Vasilevski for the case of the unit ball, we obtain a commutative algebra on Hs2(Cn) formed only by Toeplitz operators and a composition formula is obtained. Employing a natural extension for the notion of Toeplitz operators, we introduce “true-k-Toeplitz operators” acting on the true-k-Fock spaces. We provide a commutative C⋆-algebra generated by such operators, whose symbol depends on the real and imaginary parts of the complex variable in a certain sense. Dans cet article, nous construisons des algèbres commutatives générées par les opérateurs de Toeplitz sur l'espace de Segal–Bargmann Hs2(Cn) et sur les espaces true-k-Fock. En utilisant une méthode analogue à celle mise en œuvre sur les algèbres de Banach commutatives construites par N. Vasilevski, nous obtenons une algèbre commutative sur Hs2(Cn) formée uniquement par les opérateurs de Toeplitz, et une formule de composition est aussi obtenue. En utilisant une extension naturelle de la notion d'opérateur de Toeplitz, nous introduisons les opérateurs « true-k-Toeplitz » agissant sur les espaces true-k-Fock. Nous fournissons une C⋆-algèbre commutative générée par ces opérateurs, dont les symboles dépendent des parties réelle et imaginaire de la variable complexe dans un certain sens." @default.
- W2938988892 created "2019-04-25" @default.
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- W2938988892 date "2019-04-01" @default.
- W2938988892 modified "2023-09-25" @default.
- W2938988892 title "Construction of some classes of commutative Banach and C⋆-algebras of Toeplitz operators" @default.
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- W2938988892 doi "https://doi.org/10.1016/j.crma.2019.04.003" @default.
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