Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle
The first goal of this paper is to find a representation of the Fock space on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi&...
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/12/1080 |
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| author | Carlos González-Flores Luis Alfredo Dupont-García Raquiel Rufino López-Martínez Francisco Gabriel Hérnandez-Zamora |
| author_facet | Carlos González-Flores Luis Alfredo Dupont-García Raquiel Rufino López-Martínez Francisco Gabriel Hérnandez-Zamora |
| author_sort | Carlos González-Flores |
| collection | DOAJ |
| description | The first goal of this paper is to find a representation of the Fock space on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula> in terms of the weighted Bergman spaces of the projective spaces <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">CP</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">CP</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>. Also, we study the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula> algebras generated by Toeplitz operators where the symbols are taken from the following two families of functions: Firstly, the symbols depend on the moment map associated with the unit circle, and secondly, the symbols are invariant under the same action. Moreover, we analyze the commutative relations between these algebras, and we apply these results to find new commutative Banach algebras generated by Toeplitz operators on Fock space of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>. |
| first_indexed | 2024-03-08T21:01:02Z |
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| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-08T21:01:02Z |
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| spelling | doaj.art-d09beb38ece641d4a695ff1b5925b5802023-12-22T13:53:11ZengMDPI AGAxioms2075-16802023-11-011212108010.3390/axioms12121080Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit CircleCarlos González-Flores0Luis Alfredo Dupont-García1Raquiel Rufino López-Martínez2Francisco Gabriel Hérnandez-Zamora3Escuela Superior de Ingeniería Mecánica y Eléctrica Zacatenco, Instituto Politécnico Nacional, Mexico City 07738, MexicoFacultad de Matemáticas, Universidad Veracruzana, Veracruz 94294, MexicoFacultad de Matemáticas, Universidad Veracruzana, Veracruz 94294, MexicoFacultad de Matemáticas, Universidad Veracruzana, Veracruz 94294, MexicoThe first goal of this paper is to find a representation of the Fock space on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula> in terms of the weighted Bergman spaces of the projective spaces <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">CP</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">CP</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>. Also, we study the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula> algebras generated by Toeplitz operators where the symbols are taken from the following two families of functions: Firstly, the symbols depend on the moment map associated with the unit circle, and secondly, the symbols are invariant under the same action. Moreover, we analyze the commutative relations between these algebras, and we apply these results to find new commutative Banach algebras generated by Toeplitz operators on Fock space of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>.https://www.mdpi.com/2075-1680/12/12/1080Toeplitz operatorsmoment maps<i>C</i>* algebrascommutative banach algebrasfock spaces |
| spellingShingle | Carlos González-Flores Luis Alfredo Dupont-García Raquiel Rufino López-Martínez Francisco Gabriel Hérnandez-Zamora Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle Axioms Toeplitz operators moment maps <i>C</i>* algebras commutative banach algebras fock spaces |
| title | Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle |
| title_full | Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle |
| title_fullStr | Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle |
| title_full_unstemmed | Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle |
| title_short | Toeplitz Operators on Fock Space over <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi mathvariant="bold-italic">n</mi></msup></semantics></math></inline-formula> with Invariant Symbols under the Action of the Unit Circle |
| title_sort | toeplitz operators on fock space over inline formula math display inline semantics msup mi mathvariant double struck c mi mi mathvariant bold italic n mi msup semantics math inline formula with invariant symbols under the action of the unit circle |
| topic | Toeplitz operators moment maps <i>C</i>* algebras commutative banach algebras fock spaces |
| url | https://www.mdpi.com/2075-1680/12/12/1080 |
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