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

초록

Let n, m ∈ N, n, m ≥ 2 and E a Banach space. An element (x<inf>1</inf>, …, x<inf>n</inf>) ∈ 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 (x<inf>1</inf>, …, x<inf>n</inf>) ∈ En which are the norming points of T. Let (Formula presented) with a norm satisfying that {W<inf>1</inf>, …, W<inf>n</inf>} 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). Then, (Formula presented) © (2024), (VNTL Publishers). All rights reserved.

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