A look into homomorphisms between uniform algebras over a Hilbert space
We study the vector-valued spectrum \(\mathcal{M}_{u,\infty}(B_{\ell_2},B_{\ell_2})\) which is the set of nonzero algebra homomorphisms from \(\mathcal{A}_u(B_{\ell_2})\) (the algebra of uniformly continuous holomorphic functions on \(B_{\ell_2}\)) to \(\mathcal {H}^\infty(B_{\ell_2})\) (the algebra...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2021-02 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Dimant, Verónica Singer, Joaquín |
| description | We study the vector-valued spectrum \(\mathcal{M}_{u,\infty}(B_{\ell_2},B_{\ell_2})\) which is the set of nonzero algebra homomorphisms from \(\mathcal{A}_u(B_{\ell_2})\) (the algebra of uniformly continuous holomorphic functions on \(B_{\ell_2}\)) to \(\mathcal {H}^\infty(B_{\ell_2})\) (the algebra of bounded holomorphic functions on \(B_{\ell_2}\)). This set is naturally projected onto the closed unit ball of \(\mathcal {H}^\infty(B_{\ell_2}, \ell_2)\) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets. |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2489934164</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2489934164</sourcerecordid><originalsourceid>FETCH-proquest_journals_24899341643</originalsourceid><addsrcrecordid>eNqNikEOgjAQABsTE4nyh008k0BbEI7GqDzAOylmkWLpYlv0-3LwAWYOc5hZsYgLkSWl5HzDYu-HNE15ceB5LiJ2PYIheoK2gaCnccFNvfajhxbDB9HCbHVHbgRlHtg65YHe6EBBrU2LLoCf1B13bN0p4zH-ecv2l_PtVCeTo9eMPjQDzc4uqeGyrCohs0KK_64vFHA70w</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2489934164</pqid></control><display><type>article</type><title>A look into homomorphisms between uniform algebras over a Hilbert space</title><source>Free E- Journals</source><creator>Dimant, Verónica ; Singer, Joaquín</creator><creatorcontrib>Dimant, Verónica ; Singer, Joaquín</creatorcontrib><description>We study the vector-valued spectrum \(\mathcal{M}_{u,\infty}(B_{\ell_2},B_{\ell_2})\) which is the set of nonzero algebra homomorphisms from \(\mathcal{A}_u(B_{\ell_2})\) (the algebra of uniformly continuous holomorphic functions on \(B_{\ell_2}\)) to \(\mathcal {H}^\infty(B_{\ell_2})\) (the algebra of bounded holomorphic functions on \(B_{\ell_2}\)). This set is naturally projected onto the closed unit ball of \(\mathcal {H}^\infty(B_{\ell_2}, \ell_2)\) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Analytic functions ; Clusters ; Continuity (mathematics) ; Hilbert space ; Homomorphisms ; Mathematical analysis</subject><ispartof>arXiv.org, 2021-02</ispartof><rights>2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Dimant, Verónica</creatorcontrib><creatorcontrib>Singer, Joaquín</creatorcontrib><title>A look into homomorphisms between uniform algebras over a Hilbert space</title><title>arXiv.org</title><description>We study the vector-valued spectrum \(\mathcal{M}_{u,\infty}(B_{\ell_2},B_{\ell_2})\) which is the set of nonzero algebra homomorphisms from \(\mathcal{A}_u(B_{\ell_2})\) (the algebra of uniformly continuous holomorphic functions on \(B_{\ell_2}\)) to \(\mathcal {H}^\infty(B_{\ell_2})\) (the algebra of bounded holomorphic functions on \(B_{\ell_2}\)). This set is naturally projected onto the closed unit ball of \(\mathcal {H}^\infty(B_{\ell_2}, \ell_2)\) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets.</description><subject>Algebra</subject><subject>Analytic functions</subject><subject>Clusters</subject><subject>Continuity (mathematics)</subject><subject>Hilbert space</subject><subject>Homomorphisms</subject><subject>Mathematical analysis</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNikEOgjAQABsTE4nyh008k0BbEI7GqDzAOylmkWLpYlv0-3LwAWYOc5hZsYgLkSWl5HzDYu-HNE15ceB5LiJ2PYIheoK2gaCnccFNvfajhxbDB9HCbHVHbgRlHtg65YHe6EBBrU2LLoCf1B13bN0p4zH-ecv2l_PtVCeTo9eMPjQDzc4uqeGyrCohs0KK_64vFHA70w</recordid><startdate>20210212</startdate><enddate>20210212</enddate><creator>Dimant, Verónica</creator><creator>Singer, Joaquín</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20210212</creationdate><title>A look into homomorphisms between uniform algebras over a Hilbert space</title><author>Dimant, Verónica ; Singer, Joaquín</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_24899341643</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Analytic functions</topic><topic>Clusters</topic><topic>Continuity (mathematics)</topic><topic>Hilbert space</topic><topic>Homomorphisms</topic><topic>Mathematical analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Dimant, Verónica</creatorcontrib><creatorcontrib>Singer, Joaquín</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dimant, Verónica</au><au>Singer, Joaquín</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>A look into homomorphisms between uniform algebras over a Hilbert space</atitle><jtitle>arXiv.org</jtitle><date>2021-02-12</date><risdate>2021</risdate><eissn>2331-8422</eissn><abstract>We study the vector-valued spectrum \(\mathcal{M}_{u,\infty}(B_{\ell_2},B_{\ell_2})\) which is the set of nonzero algebra homomorphisms from \(\mathcal{A}_u(B_{\ell_2})\) (the algebra of uniformly continuous holomorphic functions on \(B_{\ell_2}\)) to \(\mathcal {H}^\infty(B_{\ell_2})\) (the algebra of bounded holomorphic functions on \(B_{\ell_2}\)). This set is naturally projected onto the closed unit ball of \(\mathcal {H}^\infty(B_{\ell_2}, \ell_2)\) giving rise to an associated fibering. Extending the classical notion of cluster sets introduced by I. J. Schark (1961) to the vector-valued spectrum we define vector-valued cluster sets. The aim of the article is to look at the relationship between fibers and cluster sets obtaining results regarding the existence of analytic balls into these sets.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2021-02 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_2489934164 |
| source | Free E- Journals |
| subjects | Algebra Analytic functions Clusters Continuity (mathematics) Hilbert space Homomorphisms Mathematical analysis |
| title | A look into homomorphisms between uniform algebras over a Hilbert space |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T14%3A05%3A14IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=A%20look%20into%20homomorphisms%20between%20uniform%20algebras%20over%20a%20Hilbert%20space&rft.jtitle=arXiv.org&rft.au=Dimant,%20Ver%C3%B3nica&rft.date=2021-02-12&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2489934164%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2489934164&rft_id=info:pmid/&rfr_iscdi=true |