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Originalpublikation
Bauer, W.; Rodriguez Rodriguez, M.A.: Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results. In: Complex analysis and operator theory 16 (2022), Nr. 6, 77. DOI: https://doi.org/10.1007/s11785-022-01248-1
Version im Repositorium
Zum Zitieren der Version im Repositorium verwenden Sie bitte diesen DOI:
https://doi.org/10.15488/12904
| Zusammenfassung: | |
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We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and Hardy spaces over the unit ball in Cn. As an application we discuss semi-simplicity and the spectral invariance of these algebras. The different function Hilbert spaces are dealt with in parallel in successive chapters so that a direct comparison of the results is possible. As a new aspect of the theory we define commutative Toeplitz algebras over spaces of functions in infinitely many variables and present some structural results. The paper concludes with a short list of open problems in this area of research. © 2022, The Author(s).
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| Lizenzbestimmungen: | CC BY 4.0 Unported - https://creativecommons.org/licenses/by/4.0/ |
| Publikationstyp: | Article |
| Publikationsstatus: | publishedVersion |
| Erstveröffentlichung: | 2022 |
| Schlagwörter (englisch): | Bergman and Hardy space, Commutative Banach algebras, Fock space of functions in infinitely many variables, Gaussian measure in infinite dimensions |
| Fachliche Zuordnung (DDC): | 510 | Mathematik, 004 | Informatik |
Die Publikation erscheint in Sammlung(en):
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Fakultät für Mathematik und Physik
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