DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the correspondi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Glasgow mathematical journal 2015-09, Vol.57 (3), p.693-707
1. Verfasser: CHOI, YEMON
Format: Artikel
Sprache:eng
Schlagworte:
Affine transformations
Algebra
Exposure
Mathematical analysis
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 707
container_issue 3
container_start_page 693
container_title Glasgow mathematical journal
container_volume 57
creator CHOI, YEMON
description An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line.
doi_str_mv 10.1017/S0017089514000573
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1718918699</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0017089514000573</cupid><sourcerecordid>3750730961</sourcerecordid><originalsourceid>FETCH-LOGICAL-c463t-da4e8b0970f2ebbf14c01088b9102b884881d4f04b55306246e00b4949b77e713</originalsourceid><addsrcrecordid>eNp1kEFPg0AQhTdGE2v1B3gj8eKFOlMWdveIFCoJQlMg0RNh6WLatKWy7cF_7zbtwWi8zOTNfO9lMoTcI4wQkD3lYCpw4SIFAJc5F2SA1BO2C-LtkgyOa_u4vyY3Wq-MdIwakHASz8OgSN6tKE7jIrT8ZBo-z_3cyiJrloflJIvKNCjiLDWj1EqywE8MHWSvMz8orOk8K2f5Lblq67VWd-c-JGUUFsGLnWTT2BjshnrO3l7UVHEJgkE7VlK2SBtA4FwKhLHknHKOC9oCla7rgDemngKQVFAhGVMMnSF5POXu-u7zoPS-2ix1o9brequ6g66QIRfIPSEM-vALXXWHfmuuq9ATTLjAGTcUnqim77TuVVvt-uWm7r8qhOr42OrPY43HOXvqjeyXiw_1I_pf1zcawXFM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1697950878</pqid></control><display><type>article</type><title>DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Cambridge University Press Journals Complete</source><creator>CHOI, YEMON</creator><creatorcontrib>CHOI, YEMON</creatorcontrib><description>An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line.</description><identifier>ISSN: 0017-0895</identifier><identifier>EISSN: 1469-509X</identifier><identifier>DOI: 10.1017/S0017089514000573</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Affine transformations ; Algebra ; Exposure ; Mathematical analysis</subject><ispartof>Glasgow mathematical journal, 2015-09, Vol.57 (3), p.693-707</ispartof><rights>Copyright © Glasgow Mathematical Journal Trust 2014</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c463t-da4e8b0970f2ebbf14c01088b9102b884881d4f04b55306246e00b4949b77e713</citedby><cites>FETCH-LOGICAL-c463t-da4e8b0970f2ebbf14c01088b9102b884881d4f04b55306246e00b4949b77e713</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0017089514000573/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,776,780,27901,27902,55603</link.rule.ids></links><search><creatorcontrib>CHOI, YEMON</creatorcontrib><title>DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS</title><title>Glasgow mathematical journal</title><addtitle>Glasgow Math. J</addtitle><description>An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line.</description><subject>Affine transformations</subject><subject>Algebra</subject><subject>Exposure</subject><subject>Mathematical analysis</subject><issn>0017-0895</issn><issn>1469-509X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kEFPg0AQhTdGE2v1B3gj8eKFOlMWdveIFCoJQlMg0RNh6WLatKWy7cF_7zbtwWi8zOTNfO9lMoTcI4wQkD3lYCpw4SIFAJc5F2SA1BO2C-LtkgyOa_u4vyY3Wq-MdIwakHASz8OgSN6tKE7jIrT8ZBo-z_3cyiJrloflJIvKNCjiLDWj1EqywE8MHWSvMz8orOk8K2f5Lblq67VWd-c-JGUUFsGLnWTT2BjshnrO3l7UVHEJgkE7VlK2SBtA4FwKhLHknHKOC9oCla7rgDemngKQVFAhGVMMnSF5POXu-u7zoPS-2ix1o9brequ6g66QIRfIPSEM-vALXXWHfmuuq9ATTLjAGTcUnqim77TuVVvt-uWm7r8qhOr42OrPY43HOXvqjeyXiw_1I_pf1zcawXFM</recordid><startdate>20150901</startdate><enddate>20150901</enddate><creator>CHOI, YEMON</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20150901</creationdate><title>DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS</title><author>CHOI, YEMON</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c463t-da4e8b0970f2ebbf14c01088b9102b884881d4f04b55306246e00b4949b77e713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Affine transformations</topic><topic>Algebra</topic><topic>Exposure</topic><topic>Mathematical analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>CHOI, YEMON</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies &amp; Aerospace Collection</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>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</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><collection>ProQuest Central Basic</collection><jtitle>Glasgow mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CHOI, YEMON</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS</atitle><jtitle>Glasgow mathematical journal</jtitle><addtitle>Glasgow Math. J</addtitle><date>2015-09-01</date><risdate>2015</risdate><volume>57</volume><issue>3</issue><spage>693</spage><epage>707</epage><pages>693-707</pages><issn>0017-0895</issn><eissn>1469-509X</eissn><abstract>An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0017089514000573</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0017-0895
ispartof Glasgow mathematical journal, 2015-09, Vol.57 (3), p.693-707
issn 0017-0895
1469-509X
language eng
recordid cdi_proquest_miscellaneous_1718918699
source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Cambridge University Press Journals Complete
subjects Affine transformations
Algebra
Exposure
Mathematical analysis
title DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T16%3A55%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=DIRECTLY%20FINITE%20ALGEBRAS%20OF%20PSEUDOFUNCTIONS%20ON%20LOCALLY%20COMPACT%20GROUPS&rft.jtitle=Glasgow%20mathematical%20journal&rft.au=CHOI,%20YEMON&rft.date=2015-09-01&rft.volume=57&rft.issue=3&rft.spage=693&rft.epage=707&rft.pages=693-707&rft.issn=0017-0895&rft.eissn=1469-509X&rft_id=info:doi/10.1017/S0017089514000573&rft_dat=%3Cproquest_cross%3E3750730961%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1697950878&rft_id=info:pmid/&rft_cupid=10_1017_S0017089514000573&rfr_iscdi=true