On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings
Applying a linearization theorem due to Mujica (Trans Am Math Soc 324:867–887, 1991), we study the ideals of bounded holomorphic mappings I ◦H∞ generated by composition with an operator ideal I. The bounded-holomorphic dual ideal of I is introduced and its elements are characterized as those that ad...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2024
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/15143 https://doi.org/10.1007/s00025-023-01868-9 |
| _version_ | 1789406640137568256 |
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| author | Cabrera Padilla, María De Gádor Jiménez Vargas, Antonio Ruiz Casternado, David |
| author_facet | Cabrera Padilla, María De Gádor Jiménez Vargas, Antonio Ruiz Casternado, David |
| author_sort | Cabrera Padilla, María De Gádor |
| collection | DSpace |
| description | Applying a linearization theorem due to Mujica (Trans Am Math Soc 324:867–887, 1991), we study the ideals of bounded holomorphic mappings I ◦H∞ generated by composition with an operator ideal I. The bounded-holomorphic dual ideal of I is introduced and its elements are characterized as those that admit a factorization through Idual. For complex Banach spaces E and F, we also analyze new ideals of bounded holomorphic mappings from an open subset U ⊆ E to F such as pintegral holomorphic mappings and p-nuclear holomorphic mappings with 1 ≤ p < ∞. We prove that every p-integral (p-nuclear) holomorphic mapping from U to F has relatively weakly compact (compact) range. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-15143 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2024 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-151432024-01-12T18:36:32Z On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings Cabrera Padilla, María De Gádor Jiménez Vargas, Antonio Ruiz Casternado, David Holomorphic mapping Operator ideal Linearization Factorization theorems Applying a linearization theorem due to Mujica (Trans Am Math Soc 324:867–887, 1991), we study the ideals of bounded holomorphic mappings I ◦H∞ generated by composition with an operator ideal I. The bounded-holomorphic dual ideal of I is introduced and its elements are characterized as those that admit a factorization through Idual. For complex Banach spaces E and F, we also analyze new ideals of bounded holomorphic mappings from an open subset U ⊆ E to F such as pintegral holomorphic mappings and p-nuclear holomorphic mappings with 1 ≤ p < ∞. We prove that every p-integral (p-nuclear) holomorphic mapping from U to F has relatively weakly compact (compact) range. 2024-01-12T18:36:31Z 2024-01-12T18:36:31Z 2023-03-19 info:eu-repo/semantics/article 1422-6383 http://hdl.handle.net/10835/15143 https://doi.org/10.1007/s00025-023-01868-9 en Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| spellingShingle | Holomorphic mapping Operator ideal Linearization Factorization theorems Cabrera Padilla, María De Gádor Jiménez Vargas, Antonio Ruiz Casternado, David On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings |
| title | On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings |
| title_full | On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings |
| title_fullStr | On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings |
| title_full_unstemmed | On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings |
| title_short | On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings |
| title_sort | on composition ideals and dual ideals of bounded holomorphic mappings |
| topic | Holomorphic mapping Operator ideal Linearization Factorization theorems |
| url | http://hdl.handle.net/10835/15143 https://doi.org/10.1007/s00025-023-01868-9 |
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