Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces

Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Ba...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2010-07
Hauptverfasser: Badea, Catalin, Lyubich, Yuri I
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Banach spaces
Convergence
Hilbert space
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 Badea, Catalin
Lyubich, Yuri I
description According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2074044717</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2074044717</sourcerecordid><originalsourceid>FETCH-proquest_journals_20740447173</originalsourceid><addsrcrecordid>eNqNjE0KwjAUhIMgWLR3CLi1kKatca34cwD38kxfNaVNal4qeHujeABXM8zMNxOWyKLIs00p5YylRK0QQq6VrKoiYdcjuh6DN3rFaUAdPHQcbM2BXv0QXDCaD94N6INB4q7h8EQPN6w_cT3q8A2jbyNsnCVuLN-CBX2Ph6CRFmzaQEeY_nTOlof9eXfKIvQYkcKldaO3sbpIoUpRlipXxX-rN-4vRkU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2074044717</pqid></control><display><type>article</type><title>Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces</title><source>Freely Accessible Journals</source><creator>Badea, Catalin ; Lyubich, Yuri I</creator><creatorcontrib>Badea, Catalin ; Lyubich, Yuri I</creatorcontrib><description>According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Asymptotic properties ; Banach spaces ; Convergence ; Hilbert space</subject><ispartof>arXiv.org, 2010-07</ispartof><rights>2010. 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>Badea, Catalin</creatorcontrib><creatorcontrib>Lyubich, Yuri I</creatorcontrib><title>Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces</title><title>arXiv.org</title><description>According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum.</description><subject>Asymptotic properties</subject><subject>Banach spaces</subject><subject>Convergence</subject><subject>Hilbert space</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNjE0KwjAUhIMgWLR3CLi1kKatca34cwD38kxfNaVNal4qeHujeABXM8zMNxOWyKLIs00p5YylRK0QQq6VrKoiYdcjuh6DN3rFaUAdPHQcbM2BXv0QXDCaD94N6INB4q7h8EQPN6w_cT3q8A2jbyNsnCVuLN-CBX2Ph6CRFmzaQEeY_nTOlof9eXfKIvQYkcKldaO3sbpIoUpRlipXxX-rN-4vRkU</recordid><startdate>20100730</startdate><enddate>20100730</enddate><creator>Badea, Catalin</creator><creator>Lyubich, Yuri I</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>PTHSS</scope></search><sort><creationdate>20100730</creationdate><title>Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces</title><author>Badea, Catalin ; Lyubich, Yuri I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20740447173</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Asymptotic properties</topic><topic>Banach spaces</topic><topic>Convergence</topic><topic>Hilbert space</topic><toplevel>online_resources</toplevel><creatorcontrib>Badea, Catalin</creatorcontrib><creatorcontrib>Lyubich, Yuri I</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; 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>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Badea, Catalin</au><au>Lyubich, Yuri I</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces</atitle><jtitle>arXiv.org</jtitle><date>2010-07-30</date><risdate>2010</risdate><eissn>2331-8422</eissn><abstract>According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum.</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, 2010-07
issn 2331-8422
language eng
recordid cdi_proquest_journals_2074044717
source Freely Accessible Journals
subjects Asymptotic properties
Banach spaces
Convergence
Hilbert space
title Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-30T17%3A27%3A32IST&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=Geometric,%20spectral%20and%20asymptotic%20properties%20of%20averaged%20products%20of%20projections%20in%20Banach%20spaces&rft.jtitle=arXiv.org&rft.au=Badea,%20Catalin&rft.date=2010-07-30&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2074044717%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2074044717&rft_id=info:pmid/&rfr_iscdi=true