Extreme points of Ls(2l∞) and P(2l∞)

Kim Sung Guen

doi:10.15330/cmp.13.2.289-297

Extreme points of L_s(²l_∞) and P(²l_∞)

Kim Sung Guen

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For n≥2, we show that every extreme point of the unit ball of L_s(²lⁿ _∞) is extreme in L_s(²lⁿ⁺1_∞), which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of L_s(²lⁿ _∞) is extreme in L_s(²l_∞). We also show that every extreme point of the unit ball of P(²l² _∞) is extreme in P(²lⁿ _∞). As a corollary we show that every extreme point of the unit ball of P(²l² _∞) is extreme in P(²l_∞).

Original language	English
Pages (from-to)	289-297
Number of pages	9
Journal	Carpathian Mathematical Publications
Volume	13
Issue number	2
DOIs	https://doi.org/10.15330/cmp.13.2.289-297
State	Published - 2021

Keywords

2-homogeneous polynomials on l
Extreme point
Symmetric bilinear form

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10.15330/cmp.13.2.289-297

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title = "Extreme points of Ls(2l∞) and P(2l∞)",

abstract = "For n≥2, we show that every extreme point of the unit ball of Ls(2ln ∞) is extreme in Ls(2ln+1∞), which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of Ls(2ln ∞) is extreme in Ls(2l∞). We also show that every extreme point of the unit ball of P(2l2 ∞) is extreme in P(2ln ∞). As a corollary we show that every extreme point of the unit ball of P(2l2 ∞) is extreme in P(2l∞).",

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N2 - For n≥2, we show that every extreme point of the unit ball of Ls(2ln ∞) is extreme in Ls(2ln+1∞), which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of Ls(2ln ∞) is extreme in Ls(2l∞). We also show that every extreme point of the unit ball of P(2l2 ∞) is extreme in P(2ln ∞). As a corollary we show that every extreme point of the unit ball of P(2l2 ∞) is extreme in P(2l∞).

AB - For n≥2, we show that every extreme point of the unit ball of Ls(2ln ∞) is extreme in Ls(2ln+1∞), which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of Ls(2ln ∞) is extreme in Ls(2l∞). We also show that every extreme point of the unit ball of P(2l2 ∞) is extreme in P(2ln ∞). As a corollary we show that every extreme point of the unit ball of P(2l2 ∞) is extreme in P(2l∞).

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KW - Symmetric bilinear form

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JO - Carpathian Mathematical Publications

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Extreme points of L_s(²l_∞) and P(²l_∞)

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