THE NORMING SET OF A SYMMETRIC BILINEAR FORM ON THE PLANE WITH THE SUPREMUM NORM

S. G. Kim

doi:10.30970/MS.55.2.171-180

THE NORMING SET OF A SYMMETRIC BILINEAR FORM ON THE PLANE WITH THE SUPREMUM NORM

S. G. Kim

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

17 Scopus citations

Abstract

An element (x₁,..., x_n) ϵ Eⁿ is called a norming point of T ϵ L_s(ⁿE) if ||x₁ H = · · · = ||x_n|| = 1 and |T(x₁,..., x_n)| = ||T||, where L_s(ⁿE) denotes the space of all symmetric continuous n-linear forms on E. For T ϵ Ls(ⁿE), we define Norm(T) = {(x1,..., xn) ϵ Eⁿ: (x1,..., xn) is a norming point of T}. Norm(T) is called the norming set of T. We classify Norm(T) for every T ϵ L_s (Formula presented).

Original language	English
Pages (from-to)	171-180
Number of pages	10
Journal	Matematychni Studii
Volume	55
Issue number	2
DOIs	https://doi.org/10.30970/MS.55.2.171-180
State	Published - 2021

Keywords

norming points
symmetric bilinear forms

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title = "THE NORMING SET OF A SYMMETRIC BILINEAR FORM ON THE PLANE WITH THE SUPREMUM NORM",

abstract = "An element (x1,..., xn) ϵ En is called a norming point of T ϵ Ls(nE) if ||x1 H = · · · = ||xn|| = 1 and |T(x1,..., xn)| = ||T||, where Ls(nE) denotes the space of all symmetric continuous n-linear forms on E. For T ϵ Ls(nE), we define Norm(T) = \{(x1,..., xn) ϵ En: (x1,..., xn) is a norming point of T\}. Norm(T) is called the norming set of T. We classify Norm(T) for every T ϵ Ls (Formula presented).",

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N2 - An element (x1,..., xn) ϵ En is called a norming point of T ϵ Ls(nE) if ||x1 H = · · · = ||xn|| = 1 and |T(x1,..., xn)| = ||T||, where Ls(nE) denotes the space of all symmetric continuous n-linear forms on E. For T ϵ Ls(nE), we define Norm(T) = {(x1,..., xn) ϵ En: (x1,..., xn) is a norming point of T}. Norm(T) is called the norming set of T. We classify Norm(T) for every T ϵ Ls (Formula presented).

AB - An element (x1,..., xn) ϵ En is called a norming point of T ϵ Ls(nE) if ||x1 H = · · · = ||xn|| = 1 and |T(x1,..., xn)| = ||T||, where Ls(nE) denotes the space of all symmetric continuous n-linear forms on E. For T ϵ Ls(nE), we define Norm(T) = {(x1,..., xn) ϵ En: (x1,..., xn) is a norming point of T}. Norm(T) is called the norming set of T. We classify Norm(T) for every T ϵ Ls (Formula presented).

KW - norming points

KW - symmetric bilinear forms

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DO - 10.30970/MS.55.2.171-180

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SN - 1027-4634

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JO - Matematychni Studii

JF - Matematychni Studii

IS - 2

ER -

THE NORMING SET OF A SYMMETRIC BILINEAR FORM ON THE PLANE WITH THE SUPREMUM NORM

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Keywords

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