A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators
In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A,B a numerical radius and some operator norm versions for arithmetic-geometric mean inequality are obtained, respectively as ω 2 ( A ♯ B ) ⩽ ω ( A 2 + B 2 2 ) − 1 2 inf | | x | |...
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| Veröffentlicht in: | Filomat 2016-01, Vol.30 (8), p.2139-2145 |
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| creator | Sheikhhosseinia, Alemeh |
| description | In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A,B a numerical radius and some operator norm versions for arithmetic-geometric mean inequality are obtained, respectively as
ω
2
(
A
♯
B
)
⩽
ω
(
A
2
+
B
2
2
)
−
1
2
inf
|
|
x
|
|
=
1
δ
(
x
)
,
where δ(x) = 〈(A - B)x,x〈2 , and
|
|
A
|
|
|
|
B
|
|
⩽
1
2
(
|
|
A
2
|
|
+
|
|
B
2
|
|
)
−
1
2
inf
|
|
x
|
|
=
|
|
y
|
|
=
1
δ
(
x
,
y
)
,
where, δ(x, y) = (⟨Ay, y⟩ – ⟨Bx, x⟩)2 : |
| doi_str_mv | 10.2298/FIL1608139S |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_2298_FIL1608139S</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>24899233</jstor_id><sourcerecordid>24899233</sourcerecordid><originalsourceid>FETCH-LOGICAL-c250t-5f9ce19842e0162e1382c46d5a1729fe5aae40445b8c4ff45ef2f2e6aa7b56c73</originalsourceid><addsrcrecordid>eNpN0EtLAzEUBeAgCo7VlWshe4kmN49JlkOxDxgt-NoOaXpDp7ROSaYL_72jFXF1zuLjcjmEXAt-B-Ds_WReC8OtkO7lhBSguGHcSXlKCi61YlpYfk4uct5wrsCosiCzij4ddpja4Lf02a_aQ6bvmHLbfdAu0n6NtEptv95h3wY2xW4oA6aP6H_AYo_J913Kl-Qs-m3Gq98ckbfJw-t4xurFdD6uahZA857p6AIKZxUgFwZQSAtBmZX2ogQXUXuPiiullzaoGJXGCBHQeF8utQmlHJHb492QupwTxmaf2p1Pn43gzfcIzb8RBn1z1Js8PPlHQVnnQEr5BU2nWHo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators</title><source>Jstor Complete Legacy</source><source>EZB-FREE-00999 freely available EZB journals</source><source>JSTOR Mathematics & Statistics</source><creator>Sheikhhosseinia, Alemeh</creator><creatorcontrib>Sheikhhosseinia, Alemeh</creatorcontrib><description>In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A,B a numerical radius and some operator norm versions for arithmetic-geometric mean inequality are obtained, respectively as
ω
2
(
A
♯
B
)
⩽
ω
(
A
2
+
B
2
2
)
−
1
2
inf
|
|
x
|
|
=
1
δ
(
x
)
,
where δ(x) = 〈(A - B)x,x〈2 , and
|
|
A
|
|
|
|
B
|
|
⩽
1
2
(
|
|
A
2
|
|
+
|
|
B
2
|
|
)
−
1
2
inf
|
|
x
|
|
=
|
|
y
|
|
=
1
δ
(
x
,
y
)
,
where, δ(x, y) = (⟨Ay, y⟩ – ⟨Bx, x⟩)2 :</description><identifier>ISSN: 0354-5180</identifier><identifier>EISSN: 2406-0933</identifier><identifier>DOI: 10.2298/FIL1608139S</identifier><language>eng</language><publisher>Faculty of Sciences and Mathematics, University of Niš</publisher><subject>Geometric mean ; Mathematical inequalities</subject><ispartof>Filomat, 2016-01, Vol.30 (8), p.2139-2145</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/24899233$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/24899233$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,4010,27900,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>Sheikhhosseinia, Alemeh</creatorcontrib><title>A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators</title><title>Filomat</title><description>In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A,B a numerical radius and some operator norm versions for arithmetic-geometric mean inequality are obtained, respectively as
ω
2
(
A
♯
B
)
⩽
ω
(
A
2
+
B
2
2
)
−
1
2
inf
|
|
x
|
|
=
1
δ
(
x
)
,
where δ(x) = 〈(A - B)x,x〈2 , and
|
|
A
|
|
|
|
B
|
|
⩽
1
2
(
|
|
A
2
|
|
+
|
|
B
2
|
|
)
−
1
2
inf
|
|
x
|
|
=
|
|
y
|
|
=
1
δ
(
x
,
y
)
,
where, δ(x, y) = (⟨Ay, y⟩ – ⟨Bx, x⟩)2 :</description><subject>Geometric mean</subject><subject>Mathematical inequalities</subject><issn>0354-5180</issn><issn>2406-0933</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNpN0EtLAzEUBeAgCo7VlWshe4kmN49JlkOxDxgt-NoOaXpDp7ROSaYL_72jFXF1zuLjcjmEXAt-B-Ds_WReC8OtkO7lhBSguGHcSXlKCi61YlpYfk4uct5wrsCosiCzij4ddpja4Lf02a_aQ6bvmHLbfdAu0n6NtEptv95h3wY2xW4oA6aP6H_AYo_J913Kl-Qs-m3Gq98ckbfJw-t4xurFdD6uahZA857p6AIKZxUgFwZQSAtBmZX2ogQXUXuPiiullzaoGJXGCBHQeF8utQmlHJHb492QupwTxmaf2p1Pn43gzfcIzb8RBn1z1Js8PPlHQVnnQEr5BU2nWHo</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Sheikhhosseinia, Alemeh</creator><general>Faculty of Sciences and Mathematics, University of Niš</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160101</creationdate><title>A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators</title><author>Sheikhhosseinia, Alemeh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c250t-5f9ce19842e0162e1382c46d5a1729fe5aae40445b8c4ff45ef2f2e6aa7b56c73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Geometric mean</topic><topic>Mathematical inequalities</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sheikhhosseinia, Alemeh</creatorcontrib><collection>CrossRef</collection><jtitle>Filomat</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sheikhhosseinia, Alemeh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators</atitle><jtitle>Filomat</jtitle><date>2016-01-01</date><risdate>2016</risdate><volume>30</volume><issue>8</issue><spage>2139</spage><epage>2145</epage><pages>2139-2145</pages><issn>0354-5180</issn><eissn>2406-0933</eissn><abstract>In this paper, we obtain some numerical radius inequalities for operators, in particular for positive definite operators A,B a numerical radius and some operator norm versions for arithmetic-geometric mean inequality are obtained, respectively as
ω
2
(
A
♯
B
)
⩽
ω
(
A
2
+
B
2
2
)
−
1
2
inf
|
|
x
|
|
=
1
δ
(
x
)
,
where δ(x) = 〈(A - B)x,x〈2 , and
|
|
A
|
|
|
|
B
|
|
⩽
1
2
(
|
|
A
2
|
|
+
|
|
B
2
|
|
)
−
1
2
inf
|
|
x
|
|
=
|
|
y
|
|
=
1
δ
(
x
,
y
)
,
where, δ(x, y) = (⟨Ay, y⟩ – ⟨Bx, x⟩)2 :</abstract><pub>Faculty of Sciences and Mathematics, University of Niš</pub><doi>10.2298/FIL1608139S</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0354-5180 |
| ispartof | Filomat, 2016-01, Vol.30 (8), p.2139-2145 |
| issn | 0354-5180 2406-0933 |
| language | eng |
| recordid | cdi_crossref_primary_10_2298_FIL1608139S |
| source | Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; JSTOR Mathematics & Statistics |
| subjects | Geometric mean Mathematical inequalities |
| title | A Numerical Radius Version of the Arithmetic-Geometric Mean of Operators |
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