Composition operators on vector-valued analytic function spaces: a survey
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly concentrate on the research line into qualitative properties such as...
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fttartuunivojs:oai:ojs.utlib.ee:article/17239 2023-05-15T18:41:23+02:00 Composition operators on vector-valued analytic function spaces: a survey Laitila, Jussi Tylli, Hans-Olav 2014-06-25 application/pdf http://ojs.utlib.ee/index.php/ACUTM/article/view/ACUTM.2014.18.14 https://doi.org/10.12697/ACUTM.2014.18.14 eng eng University of Tartu Press http://ojs.utlib.ee/index.php/ACUTM/article/view/ACUTM.2014.18.14/12103 http://ojs.utlib.ee/index.php/ACUTM/article/view/ACUTM.2014.18.14 doi:10.12697/ACUTM.2014.18.14 Acta et Commentationes Universitatis Tartuensis de Mathematica; Vol. 18 No. 1 (2014); 135-157 2228-4699 1406-2283 analytic functions Banach space compactness composition operator weak compactness vector-valued function 47B33 46E15 46E40 47B07 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peer-reviewed Article 2014 fttartuunivojs https://doi.org/10.12697/ACUTM.2014.18.14 2021-06-23T23:02:23Z We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly concentrate on the research line into qualitative properties such as weak compactness, initiated by Liu, Saksman and Tylli (1998), and continued in several other papers. We discuss composition operators on strong, respectively weak, spaces of vector-valued analytic functions, as well as between weak and strong spaces. As concrete examples, we review more carefully and present some new observations in the cases of vector-valued Hardy and BMOA spaces, though the study of composition operators has been extended to a wide range of spaces of vector-valued analytic functions, including spaces defined on other domains. Several open problems are stated. Article in Journal/Newspaper tylli University of Tartu: ojs.utlib.ee Acta et Commentationes Universitatis Tartuensis de Mathematica 18 1 135 157 |
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Open Polar |
collection |
University of Tartu: ojs.utlib.ee |
op_collection_id |
fttartuunivojs |
language |
English |
topic |
analytic functions Banach space compactness composition operator weak compactness vector-valued function 47B33 46E15 46E40 47B07 |
spellingShingle |
analytic functions Banach space compactness composition operator weak compactness vector-valued function 47B33 46E15 46E40 47B07 Laitila, Jussi Tylli, Hans-Olav Composition operators on vector-valued analytic function spaces: a survey |
topic_facet |
analytic functions Banach space compactness composition operator weak compactness vector-valued function 47B33 46E15 46E40 47B07 |
description |
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly concentrate on the research line into qualitative properties such as weak compactness, initiated by Liu, Saksman and Tylli (1998), and continued in several other papers. We discuss composition operators on strong, respectively weak, spaces of vector-valued analytic functions, as well as between weak and strong spaces. As concrete examples, we review more carefully and present some new observations in the cases of vector-valued Hardy and BMOA spaces, though the study of composition operators has been extended to a wide range of spaces of vector-valued analytic functions, including spaces defined on other domains. Several open problems are stated. |
format |
Article in Journal/Newspaper |
author |
Laitila, Jussi Tylli, Hans-Olav |
author_facet |
Laitila, Jussi Tylli, Hans-Olav |
author_sort |
Laitila, Jussi |
title |
Composition operators on vector-valued analytic function spaces: a survey |
title_short |
Composition operators on vector-valued analytic function spaces: a survey |
title_full |
Composition operators on vector-valued analytic function spaces: a survey |
title_fullStr |
Composition operators on vector-valued analytic function spaces: a survey |
title_full_unstemmed |
Composition operators on vector-valued analytic function spaces: a survey |
title_sort |
composition operators on vector-valued analytic function spaces: a survey |
publisher |
University of Tartu Press |
publishDate |
2014 |
url |
http://ojs.utlib.ee/index.php/ACUTM/article/view/ACUTM.2014.18.14 https://doi.org/10.12697/ACUTM.2014.18.14 |
genre |
tylli |
genre_facet |
tylli |
op_source |
Acta et Commentationes Universitatis Tartuensis de Mathematica; Vol. 18 No. 1 (2014); 135-157 2228-4699 1406-2283 |
op_relation |
http://ojs.utlib.ee/index.php/ACUTM/article/view/ACUTM.2014.18.14/12103 http://ojs.utlib.ee/index.php/ACUTM/article/view/ACUTM.2014.18.14 doi:10.12697/ACUTM.2014.18.14 |
op_doi |
https://doi.org/10.12697/ACUTM.2014.18.14 |
container_title |
Acta et Commentationes Universitatis Tartuensis de Mathematica |
container_volume |
18 |
container_issue |
1 |
container_start_page |
135 |
op_container_end_page |
157 |
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1766230867914522624 |