Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols
We describe certain C∗-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D2⊂ℂ2. Bounded measurable functions of the form cIm ζ1,Im ζ2−ζ12 are called nilpotent symbols. In this work, we consider symbols of the form aIm ζ1bIm ζ...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8855599 |
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| author | Yessica Hernández-Eliseo Josué Ramírez-Ortega Francisco G. Hernández-Zamora |
| author_facet | Yessica Hernández-Eliseo Josué Ramírez-Ortega Francisco G. Hernández-Zamora |
| author_sort | Yessica Hernández-Eliseo |
| collection | DOAJ |
| description | We describe certain C∗-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D2⊂ℂ2. Bounded measurable functions of the form cIm ζ1,Im ζ2−ζ12 are called nilpotent symbols. In this work, we consider symbols of the form aIm ζ1bIm ζ2−ζ12, where both limits lims→0+bs and lims→+∞bs exist, and as belongs to the set of piecewise continuous functions on ℝ¯=−∞,+∞ and having one-side limit values at each point of a finite set S⊂ℝ. We prove that the C∗-algebra generated by all Toeplitz operators Tab is isomorphic to CΠ¯, where Π¯=ℝ¯×ℝ¯+ and ℝ¯+=0,+∞. |
| format | Article |
| id | doaj-art-1ebed50f6f2f4062b90e7ea0e894bff5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-1ebed50f6f2f4062b90e7ea0e894bff52025-02-03T01:25:25ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/88555998855599Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent SymbolsYessica Hernández-Eliseo0Josué Ramírez-Ortega1Francisco G. Hernández-Zamora2Universidad Veracruzana, MexicoUniversidad Veracruzana, MexicoUniversidad Veracruzana, MexicoWe describe certain C∗-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D2⊂ℂ2. Bounded measurable functions of the form cIm ζ1,Im ζ2−ζ12 are called nilpotent symbols. In this work, we consider symbols of the form aIm ζ1bIm ζ2−ζ12, where both limits lims→0+bs and lims→+∞bs exist, and as belongs to the set of piecewise continuous functions on ℝ¯=−∞,+∞ and having one-side limit values at each point of a finite set S⊂ℝ. We prove that the C∗-algebra generated by all Toeplitz operators Tab is isomorphic to CΠ¯, where Π¯=ℝ¯×ℝ¯+ and ℝ¯+=0,+∞.http://dx.doi.org/10.1155/2021/8855599 |
| spellingShingle | Yessica Hernández-Eliseo Josué Ramírez-Ortega Francisco G. Hernández-Zamora Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols Journal of Function Spaces |
| title | Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols |
| title_full | Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols |
| title_fullStr | Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols |
| title_full_unstemmed | Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols |
| title_short | Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols |
| title_sort | toeplitz operators acting on true poly bergman type spaces of the two dimensional siegel domain nilpotent symbols |
| url | http://dx.doi.org/10.1155/2021/8855599 |
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