2008/06/03 by Jaegil Kim, Kim, Jaegil, Han Ju Lee +1
Computer Science · Mathematics · #46B20 #46B22 #46G25 #52A21 #Advanced Banach Space Theory #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Variational Analysis #math.CO #math.FA #msc:46B20 #msc:46B22 #msc:46G25 #msc:52A21
paper · pdf · doi:10.48550/arxiv.0806.0507
arxiv created 2008/06/03 · openalex publication_date 2008/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the variational method, it is shown that the set of all strong peak functions in a closed algebra A of Cb(K) is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we can induce the denseness of strong peak functions on other certain spaces. In case that a set of uniformly strongly exposed points of a Banach space X is a norming subset of P(n X), then the set of all strongly norm attaining elements in P(n X) is dense. In particular, the set of all points at which the norm of P(n X) is Fréchet differentiable is a dense Gδ subset. In the last part, using Reisner's graph theoretic-approach, we construct some strongly norm attaining polynomials on a CL-space with an absolute norm. Then we show that for a finite dimensional complex Banach space X with an absolute norm, its polynomial numerical indices are one if and only if X is isometric to ℓ_∞n. Moreover, we give a characterization of the set of all complex extreme points of the unit ball of a CL-space with an absolute norm.