TY - JOUR
T1 - THE NORMING SETS OF MULTILINEAR FORMS ON A CERTAIN NORMED SPACE Rn
AU - Kim, Sung Guen
N1 - Publisher Copyright:
© (2024), (VNTL Publishers). All rights reserved.
PY - 2024
Y1 - 2024
N2 - 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).
AB - 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).
KW - m-linear forms
KW - norming points
KW - normong sets
UR - http://www.scopus.com/inward/record.url?scp=85213282488&partnerID=8YFLogxK
U2 - 10.30970/ms.62.2.192-198
DO - 10.30970/ms.62.2.192-198
M3 - Article
AN - SCOPUS:85213282488
SN - 1027-4634
VL - 62
SP - 192
EP - 198
JO - Matematychni Studii
JF - Matematychni Studii
IS - 2
ER -