Difference of composition operators on weighted Bergman spaces over the half-plane
Abstract Recently, the bounded, compact and Hilbert-Schmidt difference of composition operators on the Bergman spaces over the half-plane are characterized in (Choe et al. in Trans. Am. Math. Soc., 2016, in press). Motivated by this, we give a sufficient condition when two composition operators C φ...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1149-2 |
| _version_ | 1818135590023987200 |
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| author | Maocai Wang Changbao Pang |
| author_facet | Maocai Wang Changbao Pang |
| author_sort | Maocai Wang |
| collection | DOAJ |
| description | Abstract Recently, the bounded, compact and Hilbert-Schmidt difference of composition operators on the Bergman spaces over the half-plane are characterized in (Choe et al. in Trans. Am. Math. Soc., 2016, in press). Motivated by this, we give a sufficient condition when two composition operators C φ $C_{\varphi}$ and C ψ $C_{\psi}$ are in the same path component under the operator norm topology and show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if C φ 1 $C_{\varphi_{1}}$ , C φ 2 $C_{\varphi_{2}}$ , and C φ 3 $C_{\varphi_{3}}$ are distinct and bounded, then ( C φ 1 − C φ 2 ) − ( C φ 3 − C φ 1 ) $(C_{\varphi _{1}}-C_{\varphi_{2}})-(C_{\varphi_{3}}-C_{\varphi_{1}})$ is compact if and only if both C φ 1 − C φ 2 $C_{\varphi_{1}}-C_{\varphi_{2}}$ and C φ 1 − C φ 3 $C_{\varphi _{1}}-C_{\varphi_{3}}$ are compact on weighted Bergman spaces over the half-plane. Moreover, we prove the strong continuity of composition operators semigroup induced by a one-parameter semigroup of holomorphic self-maps of half-plane. |
| first_indexed | 2024-12-11T09:26:55Z |
| format | Article |
| id | doaj.art-fb8dbc9da8364a4a8cbf434920e4ced3 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T09:26:55Z |
| publishDate | 2016-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-fb8dbc9da8364a4a8cbf434920e4ced32022-12-22T01:13:08ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-08-012016111610.1186/s13660-016-1149-2Difference of composition operators on weighted Bergman spaces over the half-planeMaocai Wang0Changbao Pang1School of Computer, China University of GeosciencesSchool of Mathematics and Statistics, Wuhan UniversityAbstract Recently, the bounded, compact and Hilbert-Schmidt difference of composition operators on the Bergman spaces over the half-plane are characterized in (Choe et al. in Trans. Am. Math. Soc., 2016, in press). Motivated by this, we give a sufficient condition when two composition operators C φ $C_{\varphi}$ and C ψ $C_{\psi}$ are in the same path component under the operator norm topology and show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if C φ 1 $C_{\varphi_{1}}$ , C φ 2 $C_{\varphi_{2}}$ , and C φ 3 $C_{\varphi_{3}}$ are distinct and bounded, then ( C φ 1 − C φ 2 ) − ( C φ 3 − C φ 1 ) $(C_{\varphi _{1}}-C_{\varphi_{2}})-(C_{\varphi_{3}}-C_{\varphi_{1}})$ is compact if and only if both C φ 1 − C φ 2 $C_{\varphi_{1}}-C_{\varphi_{2}}$ and C φ 1 − C φ 3 $C_{\varphi _{1}}-C_{\varphi_{3}}$ are compact on weighted Bergman spaces over the half-plane. Moreover, we prove the strong continuity of composition operators semigroup induced by a one-parameter semigroup of holomorphic self-maps of half-plane.http://link.springer.com/article/10.1186/s13660-016-1149-2Bergman spacecomposition operatorHilbert-Schmidtsemigroup |
| spellingShingle | Maocai Wang Changbao Pang Difference of composition operators on weighted Bergman spaces over the half-plane Journal of Inequalities and Applications Bergman space composition operator Hilbert-Schmidt semigroup |
| title | Difference of composition operators on weighted Bergman spaces over the half-plane |
| title_full | Difference of composition operators on weighted Bergman spaces over the half-plane |
| title_fullStr | Difference of composition operators on weighted Bergman spaces over the half-plane |
| title_full_unstemmed | Difference of composition operators on weighted Bergman spaces over the half-plane |
| title_short | Difference of composition operators on weighted Bergman spaces over the half-plane |
| title_sort | difference of composition operators on weighted bergman spaces over the half plane |
| topic | Bergman space composition operator Hilbert-Schmidt semigroup |
| url | http://link.springer.com/article/10.1186/s13660-016-1149-2 |
| work_keys_str_mv | AT maocaiwang differenceofcompositionoperatorsonweightedbergmanspacesoverthehalfplane AT changbaopang differenceofcompositionoperatorsonweightedbergmanspacesoverthehalfplane |