Normal Toeplitz Operators on the Bergman Space
In this paper, we give a characterization of normality of Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on the Bergman space &...
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1463 |
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| author | Sumin Kim Jongrak Lee |
| author_facet | Sumin Kim Jongrak Lee |
| author_sort | Sumin Kim |
| collection | DOAJ |
| description | In this paper, we give a characterization of normality of Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on the Bergman space <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. First, we state basic properties for Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Next, we consider the normal Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in terms of harmonic symbols <inline-formula><math display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>. Finally, we characterize the normal Toeplitz operators <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> with non-harmonic symbols acting on <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T16:40:19Z |
| format | Article |
| id | doaj.art-ff01ed2fea274e6ca3c7328b57f3d8d2 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:40:19Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-ff01ed2fea274e6ca3c7328b57f3d8d22023-11-20T12:07:15ZengMDPI AGMathematics2227-73902020-09-0189146310.3390/math8091463Normal Toeplitz Operators on the Bergman SpaceSumin Kim0Jongrak Lee1Department of Mathematics, Sungkyunkwan University, Suwon 440-746, KoreaDepartment of Mathematics, Jeju National University, Jeju 63243, KoreaIn this paper, we give a characterization of normality of Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on the Bergman space <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. First, we state basic properties for Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Next, we consider the normal Toeplitz operator <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> on <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in terms of harmonic symbols <inline-formula><math display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>. Finally, we characterize the normal Toeplitz operators <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>φ</mi></msub></semantics></math></inline-formula> with non-harmonic symbols acting on <inline-formula><math display="inline"><semantics><mrow><msup><mi>A</mi><mn>2</mn></msup><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/8/9/1463Toeplitz operatornormal operatorBergman space |
| spellingShingle | Sumin Kim Jongrak Lee Normal Toeplitz Operators on the Bergman Space Mathematics Toeplitz operator normal operator Bergman space |
| title | Normal Toeplitz Operators on the Bergman Space |
| title_full | Normal Toeplitz Operators on the Bergman Space |
| title_fullStr | Normal Toeplitz Operators on the Bergman Space |
| title_full_unstemmed | Normal Toeplitz Operators on the Bergman Space |
| title_short | Normal Toeplitz Operators on the Bergman Space |
| title_sort | normal toeplitz operators on the bergman space |
| topic | Toeplitz operator normal operator Bergman space |
| url | https://www.mdpi.com/2227-7390/8/9/1463 |
| work_keys_str_mv | AT suminkim normaltoeplitzoperatorsonthebergmanspace AT jongraklee normaltoeplitzoperatorsonthebergmanspace |