Extremal Homogeneous Polynomials on Real Normed Spaces
If Pis a continuous m-homogeneous polynomial on a real normed space and Pis the associated symmetric m-linear form, the ratio ‖ P‖/‖ P‖ always lies between 1 and m m / m!. We show that, as in the complex case investigated by Sarantopoulos (1987, Proc. Amer. Math. Soc. 99, 340–346), there are P'...
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| Veröffentlicht in: | Journal of approximation theory 1999-04, Vol.97 (2), p.201-213 |
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| container_title | Journal of approximation theory |
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| creator | Kirwan, Pádraig Sarantopoulos, Yannis Tonge, Andrew M |
| description | If
Pis a continuous
m-homogeneous polynomial on a real normed space and
Pis the associated symmetric
m-linear form, the ratio ‖
P‖/‖
P‖ always lies between 1 and
m
m
/
m!. We show that, as in the complex case investigated by Sarantopoulos (1987,
Proc. Amer. Math. Soc.
99, 340–346), there are
P's for which ‖
P‖/‖
P‖=
m
m
/
m! and for which
Pachieves norm if and only if the normed space contains an isometric copy of ℓ
m
1. However, unlike the complex case, we find a plentiful supply of such polynomials provided
m⩾4. |
| doi_str_mv | 10.1006/jath.1996.3273 |
| format | Article |
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Pis a continuous
m-homogeneous polynomial on a real normed space and
Pis the associated symmetric
m-linear form, the ratio ‖
P‖/‖
P‖ always lies between 1 and
m
m
/
m!. We show that, as in the complex case investigated by Sarantopoulos (1987,
Proc. Amer. Math. Soc.
99, 340–346), there are
P's for which ‖
P‖/‖
P‖=
m
m
/
m! and for which
Pachieves norm if and only if the normed space contains an isometric copy of ℓ
m
1. However, unlike the complex case, we find a plentiful supply of such polynomials provided
m⩾4.</description><identifier>ISSN: 0021-9045</identifier><identifier>EISSN: 1096-0430</identifier><identifier>DOI: 10.1006/jath.1996.3273</identifier><language>eng</language><publisher>Elsevier Inc</publisher><ispartof>Journal of approximation theory, 1999-04, Vol.97 (2), p.201-213</ispartof><rights>1999 Academic Press</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-c428c7582fef5f4b95d3262f8ef7c69538e1244a31b48d7b30695796595a649f3</citedby><cites>FETCH-LOGICAL-c326t-c428c7582fef5f4b95d3262f8ef7c69538e1244a31b48d7b30695796595a649f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0021904596932736$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Kirwan, Pádraig</creatorcontrib><creatorcontrib>Sarantopoulos, Yannis</creatorcontrib><creatorcontrib>Tonge, Andrew M</creatorcontrib><title>Extremal Homogeneous Polynomials on Real Normed Spaces</title><title>Journal of approximation theory</title><description>If
Pis a continuous
m-homogeneous polynomial on a real normed space and
Pis the associated symmetric
m-linear form, the ratio ‖
P‖/‖
P‖ always lies between 1 and
m
m
/
m!. We show that, as in the complex case investigated by Sarantopoulos (1987,
Proc. Amer. Math. Soc.
99, 340–346), there are
P's for which ‖
P‖/‖
P‖=
m
m
/
m! and for which
Pachieves norm if and only if the normed space contains an isometric copy of ℓ
m
1. However, unlike the complex case, we find a plentiful supply of such polynomials provided
m⩾4.</description><issn>0021-9045</issn><issn>1096-0430</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNp1j0tLxDAUhYMoOI5uXfcPtN482yxlGB1hUPGxDml6ox3aZkiqOP_elnHr6sI5fIf7EXJNoaAA6mZnx8-Caq0Kzkp-QhYUtMpBcDglCwBGcw1CnpOLlHYAlEpJF0Stf8aIve2yTejDBw4YvlL2HLrDEPrWdikLQ_aCU_8YYo9N9rq3DtMlOfNTiVd_d0ne79Zvq02-fbp_WN1uc8eZGnMnWOVKWTGPXnpRa9lMOfMV-tIpLXmFlAlhOa1F1ZQ1hykstZJaWiW050tSHHddDClF9GYf297Gg6FgZmszW5vZ2szWE1AdAZy--m4xmuRaHBw2bUQ3mia0_6G_Gg9dRw</recordid><startdate>19990401</startdate><enddate>19990401</enddate><creator>Kirwan, Pádraig</creator><creator>Sarantopoulos, Yannis</creator><creator>Tonge, Andrew M</creator><general>Elsevier Inc</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19990401</creationdate><title>Extremal Homogeneous Polynomials on Real Normed Spaces</title><author>Kirwan, Pádraig ; Sarantopoulos, Yannis ; Tonge, Andrew M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-c428c7582fef5f4b95d3262f8ef7c69538e1244a31b48d7b30695796595a649f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kirwan, Pádraig</creatorcontrib><creatorcontrib>Sarantopoulos, Yannis</creatorcontrib><creatorcontrib>Tonge, Andrew M</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><jtitle>Journal of approximation theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kirwan, Pádraig</au><au>Sarantopoulos, Yannis</au><au>Tonge, Andrew M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extremal Homogeneous Polynomials on Real Normed Spaces</atitle><jtitle>Journal of approximation theory</jtitle><date>1999-04-01</date><risdate>1999</risdate><volume>97</volume><issue>2</issue><spage>201</spage><epage>213</epage><pages>201-213</pages><issn>0021-9045</issn><eissn>1096-0430</eissn><abstract>If
Pis a continuous
m-homogeneous polynomial on a real normed space and
Pis the associated symmetric
m-linear form, the ratio ‖
P‖/‖
P‖ always lies between 1 and
m
m
/
m!. We show that, as in the complex case investigated by Sarantopoulos (1987,
Proc. Amer. Math. Soc.
99, 340–346), there are
P's for which ‖
P‖/‖
P‖=
m
m
/
m! and for which
Pachieves norm if and only if the normed space contains an isometric copy of ℓ
m
1. However, unlike the complex case, we find a plentiful supply of such polynomials provided
m⩾4.</abstract><pub>Elsevier Inc</pub><doi>10.1006/jath.1996.3273</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| title | Extremal Homogeneous Polynomials on Real Normed Spaces |
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