THE NORMING SETS OF MULTILINEAR FORMS ON A CERTAIN NORMED SPACE Rn

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Abstract

Let n, m ∈ N, n, m ≥ 2 and E a Banach space. An element (x1, …, xn) ∈ En is called a norming point of (Formula presented) and (Formula presented), where L(nE) denotes the space of all continuous n-linear forms on E. For (Formula presented), we define Norm(T) as the set of all (x1, …, xn) ∈ En which are the norming points of T. Let (Formula presented) with a norm satisfying that {W1, …, Wn} forms a basis and the set of all extreme points of (Formula presented). In the paper we characterize Norm(T) for every (Formula presented) as follows: Let (Formula presented) such that (Formula presented) and A is the Cartesian product of the set {1,…,n}, M is the set of indices (i1,…,im) ∈ A such that (Formula presented).

Original languageEnglish
Pages (from-to)192-198
Number of pages7
JournalMatematychni Studii
Volume62
Issue number2
DOIs
StatePublished - 2024

Keywords

  • m-linear forms
  • norming points
  • normong sets

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