Norm-Peak Multilinear Forms on the Plane with the Rotated Supremum Norm
Let ≥ 2. A continuous -linear form on a Banach space is called norm-peak if there is a unique ( 1 , … , ) ∈ such that ║ 1 ║ = … = ║ ║ = 1 and for the multilinear operator norm it holds ‖ ‖ = | ( 1 , … , )|. Let 0 ≤ ≤ = ℝ 2 with the rotated supremum norm ‖( , )‖ (∞, ) = max {| cos + sin |, | sin − co...
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| Veröffentlicht in: | Mathematica Pannonica 2024-12, Vol.30_NS4 (2), p.116-121 |
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| container_title | Mathematica Pannonica |
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| creator | Kim, Sung Guen |
| description | Let ≥ 2. A continuous -linear form on a Banach space is called norm-peak if there is a unique ( 1 , … , ) ∈ such that ║ 1 ║ = … = ║ ║ = 1 and for the multilinear operator norm it holds ‖ ‖ = | ( 1 , … , )|.
Let 0 ≤ ≤ = ℝ 2 with the rotated supremum norm ‖( , )‖ (∞, ) = max {| cos + sin |, | sin − cos |}.
In this note, we characterize all norm-peak multilinear forms on . As a corollary we characterize all norm-peak multilinear forms on = ℝ 2 with the -norm for = 1, ∞. |
| doi_str_mv | 10.1556/314.2024.00012 |
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Let 0 ≤ ≤ = ℝ 2 with the rotated supremum norm ‖( , )‖ (∞, ) = max {| cos + sin |, | sin − cos |}.
In this note, we characterize all norm-peak multilinear forms on . As a corollary we characterize all norm-peak multilinear forms on = ℝ 2 with the -norm for = 1, ∞.</description><identifier>ISSN: 0865-2090</identifier><identifier>EISSN: 2786-0752</identifier><identifier>DOI: 10.1556/314.2024.00012</identifier><language>eng</language><ispartof>Mathematica Pannonica, 2024-12, Vol.30_NS4 (2), p.116-121</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c792-6991f23333066ecc6126acbc40f4fb6f8bf8782507a4ba7b28d980e209364d323</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,864,27924,27925</link.rule.ids></links><search><creatorcontrib>Kim, Sung Guen</creatorcontrib><title>Norm-Peak Multilinear Forms on the Plane with the Rotated Supremum Norm</title><title>Mathematica Pannonica</title><description>Let ≥ 2. A continuous -linear form on a Banach space is called norm-peak if there is a unique ( 1 , … , ) ∈ such that ║ 1 ║ = … = ║ ║ = 1 and for the multilinear operator norm it holds ‖ ‖ = | ( 1 , … , )|.
Let 0 ≤ ≤ = ℝ 2 with the rotated supremum norm ‖( , )‖ (∞, ) = max {| cos + sin |, | sin − cos |}.
In this note, we characterize all norm-peak multilinear forms on . As a corollary we characterize all norm-peak multilinear forms on = ℝ 2 with the -norm for = 1, ∞.</description><issn>0865-2090</issn><issn>2786-0752</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNotkMtOwzAURC0EEqWwZe0fSLh-O0tU0VKpQAXdW45jq4E8KjsR4u9JCrMZzSxGo4PQPYGcCCEfGOE5BcpzACD0Ai2o0jIDJeglWoCWIqNQwDW6SekTgINgaoE2r31ss723X_hlbIa6qTtvI15PbcJ9h4ejx_vGdh5_18PxHN_7wQ6-wh_jKfp2bPE8cYuugm2Sv_v3JTqsnw6r52z3ttmuHneZUwXNZFGQQNkkkNI7JwmV1pWOQ-ChlEGXQStNBSjLS6tKqqtCg59-M8krRtkS5X-zLvYpRR_MKdatjT-GgJkpmImCmSmYMwX2CwUXTfA</recordid><startdate>20241218</startdate><enddate>20241218</enddate><creator>Kim, Sung Guen</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20241218</creationdate><title>Norm-Peak Multilinear Forms on the Plane with the Rotated Supremum Norm</title><author>Kim, Sung Guen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c792-6991f23333066ecc6126acbc40f4fb6f8bf8782507a4ba7b28d980e209364d323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, Sung Guen</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematica Pannonica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, Sung Guen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Norm-Peak Multilinear Forms on the Plane with the Rotated Supremum Norm</atitle><jtitle>Mathematica Pannonica</jtitle><date>2024-12-18</date><risdate>2024</risdate><volume>30_NS4</volume><issue>2</issue><spage>116</spage><epage>121</epage><pages>116-121</pages><issn>0865-2090</issn><eissn>2786-0752</eissn><abstract>Let ≥ 2. A continuous -linear form on a Banach space is called norm-peak if there is a unique ( 1 , … , ) ∈ such that ║ 1 ║ = … = ║ ║ = 1 and for the multilinear operator norm it holds ‖ ‖ = | ( 1 , … , )|.
Let 0 ≤ ≤ = ℝ 2 with the rotated supremum norm ‖( , )‖ (∞, ) = max {| cos + sin |, | sin − cos |}.
In this note, we characterize all norm-peak multilinear forms on . As a corollary we characterize all norm-peak multilinear forms on = ℝ 2 with the -norm for = 1, ∞.</abstract><doi>10.1556/314.2024.00012</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| title | Norm-Peak Multilinear Forms on the Plane with the Rotated Supremum Norm |
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