An asymmetric Kadison’s inequality

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison’s inequality and several operator versions of Chebyshev’s inequality. We also discuss well-known results around the matrix geometric mean and connect it with complex interpolation....

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2010-09, Vol.433 (3), p.499-510
Main Authors: Bourin, Jean-Christophe, Ricard, Éric
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Functional Analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Matrix geometric mean
Operator inequalities
Operator theory
Positive linear maps
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033
cites cdi_FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033
container_end_page 510
container_issue 3
container_start_page 499
container_title Linear algebra and its applications
container_volume 433
creator Bourin, Jean-Christophe
Ricard, Éric
description Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison’s inequality and several operator versions of Chebyshev’s inequality. We also discuss well-known results around the matrix geometric mean and connect it with complex interpolation.
doi_str_mv 10.1016/j.laa.2010.03.015
format article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00475220v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0024379510001345</els_id><sourcerecordid>oai_HAL_hal_00475220v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033</originalsourceid><addsrcrecordid>eNp9kL9OwzAQxi0EEqXwAGwdYGBIOP9NIqYKAUVUYoHZOhxbuEqTYodK3XgNXo8nwVFQR6bTnX7f3XcfIecUcgpUXa_yBjFnkHrgOVB5QCa0LHhGS6kOyQSAiYwXlTwmJzGuAEAUwCbkYt7OMO7Wa9sHb2ZPWPvYtT9f33HmW_vxiY3vd6fkyGET7dlfnZLX-7uX20W2fH54vJ0vMyNA9JkDUSHW1tVOidpaIbHiVkpFS8FAKUBjKw5vBnjpXGEUlJyCqg0timSI8ym5Gve-Y6M3wa8x7HSHXi_mSz3MBteSMdjSxNKRNaGLMVi3F1DQQyR6pVMkeohEA9cpkqS5HDUbjAYbF7A1Pu6FjJWqrApI3M3I2fTs1tugo_G2Nbb2wZpe153_58ovTx50kQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>An asymmetric Kadison’s inequality</title><source>ScienceDirect Freedom Collection</source><creator>Bourin, Jean-Christophe ; Ricard, Éric</creator><creatorcontrib>Bourin, Jean-Christophe ; Ricard, Éric</creatorcontrib><description>Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison’s inequality and several operator versions of Chebyshev’s inequality. We also discuss well-known results around the matrix geometric mean and connect it with complex interpolation.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2010.03.015</identifier><identifier>CODEN: LAAPAW</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Algebra ; Exact sciences and technology ; Functional Analysis ; Linear and multilinear algebra, matrix theory ; Mathematical analysis ; Mathematics ; Matrix geometric mean ; Operator inequalities ; Operator theory ; Positive linear maps ; Sciences and techniques of general use</subject><ispartof>Linear algebra and its applications, 2010-09, Vol.433 (3), p.499-510</ispartof><rights>2010 Elsevier Inc.</rights><rights>2015 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033</citedby><cites>FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=22868970$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00475220$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bourin, Jean-Christophe</creatorcontrib><creatorcontrib>Ricard, Éric</creatorcontrib><title>An asymmetric Kadison’s inequality</title><title>Linear algebra and its applications</title><description>Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison’s inequality and several operator versions of Chebyshev’s inequality. We also discuss well-known results around the matrix geometric mean and connect it with complex interpolation.</description><subject>Algebra</subject><subject>Exact sciences and technology</subject><subject>Functional Analysis</subject><subject>Linear and multilinear algebra, matrix theory</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Matrix geometric mean</subject><subject>Operator inequalities</subject><subject>Operator theory</subject><subject>Positive linear maps</subject><subject>Sciences and techniques of general use</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kL9OwzAQxi0EEqXwAGwdYGBIOP9NIqYKAUVUYoHZOhxbuEqTYodK3XgNXo8nwVFQR6bTnX7f3XcfIecUcgpUXa_yBjFnkHrgOVB5QCa0LHhGS6kOyQSAiYwXlTwmJzGuAEAUwCbkYt7OMO7Wa9sHb2ZPWPvYtT9f33HmW_vxiY3vd6fkyGET7dlfnZLX-7uX20W2fH54vJ0vMyNA9JkDUSHW1tVOidpaIbHiVkpFS8FAKUBjKw5vBnjpXGEUlJyCqg0timSI8ym5Gve-Y6M3wa8x7HSHXi_mSz3MBteSMdjSxNKRNaGLMVi3F1DQQyR6pVMkeohEA9cpkqS5HDUbjAYbF7A1Pu6FjJWqrApI3M3I2fTs1tugo_G2Nbb2wZpe153_58ovTx50kQ</recordid><startdate>20100901</startdate><enddate>20100901</enddate><creator>Bourin, Jean-Christophe</creator><creator>Ricard, Éric</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope></search><sort><creationdate>20100901</creationdate><title>An asymmetric Kadison’s inequality</title><author>Bourin, Jean-Christophe ; Ricard, Éric</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Exact sciences and technology</topic><topic>Functional Analysis</topic><topic>Linear and multilinear algebra, matrix theory</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Matrix geometric mean</topic><topic>Operator inequalities</topic><topic>Operator theory</topic><topic>Positive linear maps</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bourin, Jean-Christophe</creatorcontrib><creatorcontrib>Ricard, Éric</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bourin, Jean-Christophe</au><au>Ricard, Éric</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An asymmetric Kadison’s inequality</atitle><jtitle>Linear algebra and its applications</jtitle><date>2010-09-01</date><risdate>2010</risdate><volume>433</volume><issue>3</issue><spage>499</spage><epage>510</epage><pages>499-510</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><coden>LAAPAW</coden><abstract>Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison’s inequality and several operator versions of Chebyshev’s inequality. We also discuss well-known results around the matrix geometric mean and connect it with complex interpolation.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2010.03.015</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0024-3795
ispartof Linear algebra and its applications, 2010-09, Vol.433 (3), p.499-510
issn 0024-3795
1873-1856
language eng
recordid cdi_hal_primary_oai_HAL_hal_00475220v1
source ScienceDirect Freedom Collection
subjects Algebra
Exact sciences and technology
Functional Analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Matrix geometric mean
Operator inequalities
Operator theory
Positive linear maps
Sciences and techniques of general use
title An asymmetric Kadison’s inequality
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T19%3A32%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20asymmetric%20Kadison%E2%80%99s%20inequality&rft.jtitle=Linear%20algebra%20and%20its%20applications&rft.au=Bourin,%20Jean-Christophe&rft.date=2010-09-01&rft.volume=433&rft.issue=3&rft.spage=499&rft.epage=510&rft.pages=499-510&rft.issn=0024-3795&rft.eissn=1873-1856&rft.coden=LAAPAW&rft_id=info:doi/10.1016/j.laa.2010.03.015&rft_dat=%3Chal_cross%3Eoai_HAL_hal_00475220v1%3C/hal_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c404t-f049aadefdf64dee45a93e55618420660ace930bc038ff7c6083106dc17700033%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true