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Non-linear positive maps between C-algebras
We present some properties of (not necessarily linear) positive maps between -algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between -algebras. Then we give some basic properties and fundamental inequalities related to such maps. Next, we study n-positive maps (...
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| Published in: | Linear & multilinear algebra 2020-08, Vol.68 (8), p.1501-1517 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c338t-cb95e68e00711bc4f74c304087fc3fb4b923df21f520e28017a86fc9df70470c3 |
| container_end_page | 1517 |
| container_issue | 8 |
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| container_title | Linear & multilinear algebra |
| container_volume | 68 |
| creator | Dadkhah, Ali Moslehian, Mohammad Sal |
| description | We present some properties of (not necessarily linear) positive maps between
-algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between
-algebras. Then we give some basic properties and fundamental inequalities related to such maps. Next, we study n-positive maps (
). We show that if for a unital 3-positive map
between unital
-algebras and some
equality
holds, then
for all
. In addition, we prove that for a certain class of unital positive maps
between unital
-algebras, the inequality
holds for all
and all positive elements
if and only if
. Furthermore, we show that if for some α in the unit ball of
or in
with
, the equality
holds, then Φ is additive on positive elements of
. Moreover, we present a mild condition for a 6-positive map, which ensures its linearity. |
| doi_str_mv | 10.1080/03081087.2018.1547357 |
| format | article |
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-algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between
-algebras. Then we give some basic properties and fundamental inequalities related to such maps. Next, we study n-positive maps (
). We show that if for a unital 3-positive map
between unital
-algebras and some
equality
holds, then
for all
. In addition, we prove that for a certain class of unital positive maps
between unital
-algebras, the inequality
holds for all
and all positive elements
if and only if
. Furthermore, we show that if for some α in the unit ball of
or in
with
, the equality
holds, then Φ is additive on positive elements of
. Moreover, we present a mild condition for a 6-positive map, which ensures its linearity.</description><identifier>ISSN: 0308-1087</identifier><identifier>EISSN: 1563-5139</identifier><identifier>DOI: 10.1080/03081087.2018.1547357</identifier><language>eng</language><publisher>Abingdon: Taylor & Francis</publisher><subject>Algebra ; Lieb map ; Linearity ; n-positive map ; nonlinear map ; superadditive</subject><ispartof>Linear & multilinear algebra, 2020-08, Vol.68 (8), p.1501-1517</ispartof><rights>2018 Informa UK Limited, trading as Taylor & Francis Group 2018</rights><rights>2018 Informa UK Limited, trading as Taylor & Francis Group</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c338t-cb95e68e00711bc4f74c304087fc3fb4b923df21f520e28017a86fc9df70470c3</citedby><cites>FETCH-LOGICAL-c338t-cb95e68e00711bc4f74c304087fc3fb4b923df21f520e28017a86fc9df70470c3</cites><orcidid>0000-0001-7905-528X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Dadkhah, Ali</creatorcontrib><creatorcontrib>Moslehian, Mohammad Sal</creatorcontrib><title>Non-linear positive maps between C-algebras</title><title>Linear & multilinear algebra</title><description>We present some properties of (not necessarily linear) positive maps between
-algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between
-algebras. Then we give some basic properties and fundamental inequalities related to such maps. Next, we study n-positive maps (
). We show that if for a unital 3-positive map
between unital
-algebras and some
equality
holds, then
for all
. In addition, we prove that for a certain class of unital positive maps
between unital
-algebras, the inequality
holds for all
and all positive elements
if and only if
. Furthermore, we show that if for some α in the unit ball of
or in
with
, the equality
holds, then Φ is additive on positive elements of
. Moreover, we present a mild condition for a 6-positive map, which ensures its linearity.</description><subject>Algebra</subject><subject>Lieb map</subject><subject>Linearity</subject><subject>n-positive map</subject><subject>nonlinear map</subject><subject>superadditive</subject><issn>0308-1087</issn><issn>1563-5139</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKs_QRhwKan35tFkdkrxBUU3ug6ZNJEp08mYTC39987QunV17-I758BHyDXCDEHDHXDQw6NmDFDPUArFpTohE5RzTiXy8pRMRoaO0Dm5yHkNAAK5nJDbt9jSpm69TUUXc93XP77Y2C4Xle933rfFgtrmy1fJ5ktyFmyT_dXxTsnn0-PH4oUu359fFw9L6jjXPXVVKf1cewCFWDkRlHAcxLAdHA-VqErGV4FhkAw804DK6nlw5SooEAocn5KbQ2-X4vfW596s4za1w6RhQiDjqFU5UPJAuRRzTj6YLtUbm_YGwYxezJ8XM3oxRy9D7v6Qq9sQ08buYmpWprf7JqaQbOvqbPj_Fb8CPmd9</recordid><startdate>20200802</startdate><enddate>20200802</enddate><creator>Dadkhah, Ali</creator><creator>Moslehian, Mohammad Sal</creator><general>Taylor & Francis</general><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-7905-528X</orcidid></search><sort><creationdate>20200802</creationdate><title>Non-linear positive maps between C-algebras</title><author>Dadkhah, Ali ; Moslehian, Mohammad Sal</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-cb95e68e00711bc4f74c304087fc3fb4b923df21f520e28017a86fc9df70470c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algebra</topic><topic>Lieb map</topic><topic>Linearity</topic><topic>n-positive map</topic><topic>nonlinear map</topic><topic>superadditive</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dadkhah, Ali</creatorcontrib><creatorcontrib>Moslehian, Mohammad Sal</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science 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><jtitle>Linear & multilinear algebra</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dadkhah, Ali</au><au>Moslehian, Mohammad Sal</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-linear positive maps between C-algebras</atitle><jtitle>Linear & multilinear algebra</jtitle><date>2020-08-02</date><risdate>2020</risdate><volume>68</volume><issue>8</issue><spage>1501</spage><epage>1517</epage><pages>1501-1517</pages><issn>0308-1087</issn><eissn>1563-5139</eissn><abstract>We present some properties of (not necessarily linear) positive maps between
-algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between
-algebras. Then we give some basic properties and fundamental inequalities related to such maps. Next, we study n-positive maps (
). We show that if for a unital 3-positive map
between unital
-algebras and some
equality
holds, then
for all
. In addition, we prove that for a certain class of unital positive maps
between unital
-algebras, the inequality
holds for all
and all positive elements
if and only if
. Furthermore, we show that if for some α in the unit ball of
or in
with
, the equality
holds, then Φ is additive on positive elements of
. Moreover, we present a mild condition for a 6-positive map, which ensures its linearity.</abstract><cop>Abingdon</cop><pub>Taylor & Francis</pub><doi>10.1080/03081087.2018.1547357</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0001-7905-528X</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0308-1087 |
| ispartof | Linear & multilinear algebra, 2020-08, Vol.68 (8), p.1501-1517 |
| issn | 0308-1087 1563-5139 |
| language | eng |
| recordid | cdi_crossref_primary_10_1080_03081087_2018_1547357 |
| source | Taylor and Francis Science and Technology Collection |
| subjects | Algebra Lieb map Linearity n-positive map nonlinear map superadditive |
| title | Non-linear positive maps between C-algebras |
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