TY - JOUR
T1 - The Norming Sets ofLml1n
AU - Kim, Sung Guen
N1 - Publisher Copyright:
© Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/8
Y1 - 2024/8
N2 - Let n ∈ ℕ, n ≥ 2. An element (x1,…,xn) ∈ En is called a norming point of T ∈ LnE if ||x1|| = … = ||xn|| = 1 and |T(x1,…,xn)| = ||T||, where ℒ(nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ (nE), we define (Formula presented.) The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ Lml1n, where l1n=Rn with the l1-norm. As applications, we classify Norm(T) for every T ∈ Lml1n with n = 2, 3 and m = 2.
AB - Let n ∈ ℕ, n ≥ 2. An element (x1,…,xn) ∈ En is called a norming point of T ∈ LnE if ||x1|| = … = ||xn|| = 1 and |T(x1,…,xn)| = ||T||, where ℒ(nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ (nE), we define (Formula presented.) The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ Lml1n, where l1n=Rn with the l1-norm. As applications, we classify Norm(T) for every T ∈ Lml1n with n = 2, 3 and m = 2.
UR - http://www.scopus.com/inward/record.url?scp=85203263071&partnerID=8YFLogxK
U2 - 10.1007/s11253-024-02329-4
DO - 10.1007/s11253-024-02329-4
M3 - Article
AN - SCOPUS:85203263071
SN - 0041-5995
VL - 76
SP - 426
EP - 442
JO - Ukrainian Mathematical Journal
JF - Ukrainian Mathematical Journal
IS - 3
ER -