The unit ball of ℘(2l22)

Yun Sung Choi; Sung Guen Kim

doi:10.1007/s000130050292

The unit ball of ℘(²l²₂)

Yun Sung Choi, Sung Guen Kim

Pohang University of Science and Technology

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

62 Scopus citations

Abstract

We classify extreme points and smooth points of the unit ball of the space ℘(²l²₂) of all 2-homogeneous polynomials on the 2-dimensional real Hilbert space l²₂ and show that the unit sphere of ℘(²l²₂) is the disjoint union of the set of extreme points of its unit ball and the set of smooth ones. We also obtain explicit formulas for the norm of f ∈ ℘(²l²_p)*(p = 1, 2, ∞).

Original language	English
Pages (from-to)	472-480
Number of pages	9
Journal	Archiv der Mathematik
Volume	71
Issue number	6
DOIs	https://doi.org/10.1007/s000130050292
State	Published - 2 Dec 1998

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title = "The unit ball of ℘(2l22)",

abstract = "We classify extreme points and smooth points of the unit ball of the space ℘(2l22) of all 2-homogeneous polynomials on the 2-dimensional real Hilbert space l22 and show that the unit sphere of ℘(2l22) is the disjoint union of the set of extreme points of its unit ball and the set of smooth ones. We also obtain explicit formulas for the norm of f ∈ ℘(2l2p)*(p = 1, 2, ∞).",

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N2 - We classify extreme points and smooth points of the unit ball of the space ℘(2l22) of all 2-homogeneous polynomials on the 2-dimensional real Hilbert space l22 and show that the unit sphere of ℘(2l22) is the disjoint union of the set of extreme points of its unit ball and the set of smooth ones. We also obtain explicit formulas for the norm of f ∈ ℘(2l2p)*(p = 1, 2, ∞).

AB - We classify extreme points and smooth points of the unit ball of the space ℘(2l22) of all 2-homogeneous polynomials on the 2-dimensional real Hilbert space l22 and show that the unit sphere of ℘(2l22) is the disjoint union of the set of extreme points of its unit ball and the set of smooth ones. We also obtain explicit formulas for the norm of f ∈ ℘(2l2p)*(p = 1, 2, ∞).

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The unit ball of ℘(²l²₂)

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