TY - JOUR
T1 - The Norming Set of a Bilinear Form on R2 with the Octagonal Norm
AU - Kim, Sung Guen
AU - Lee, Chang Yeol
AU - Jeong, Ukje
N1 - Publisher Copyright:
© Heldermann Verlag.
PY - 2023
Y1 - 2023
N2 - An element (x1, . . ., xn) ∈ En is called a norming point of T ∈ L(nE) 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 Norm (T) = {(x1, . . ., xn) ∈ En : (x1, . . ., xn) is a norming point of T}. Let R2o(w) denote R2 with the octagonal norm with weight 0 < w ≠ 1 ∥(x, y)∥o(w) = max n |x| + w|y|, |y| + w|x| o . In this paper we classify Norm (T) for every T ∈ L(2R2o(w)) with weight 0 < w ≠ 1.
AB - An element (x1, . . ., xn) ∈ En is called a norming point of T ∈ L(nE) 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 Norm (T) = {(x1, . . ., xn) ∈ En : (x1, . . ., xn) is a norming point of T}. Let R2o(w) denote R2 with the octagonal norm with weight 0 < w ≠ 1 ∥(x, y)∥o(w) = max n |x| + w|y|, |y| + w|x| o . In this paper we classify Norm (T) for every T ∈ L(2R2o(w)) with weight 0 < w ≠ 1.
KW - bilinear forms
KW - Norming points
UR - http://www.scopus.com/inward/record.url?scp=85178340403&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85178340403
SN - 0944-6532
VL - 30
SP - 111
EP - 130
JO - Journal of Convex Analysis
JF - Journal of Convex Analysis
IS - 1
ER -