2018/02/28 by Debmalya Sain, Debmalya Sain, Sain, Debmalya
Computer Science · Mathematics · #46B20 #47A05 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B20 #msc:47A05
paper · pdf · doi:10.48550/arxiv.1802.10439
openalex publication_date 2018/02/28 · arxiv created 2018/03/16 · arxiv updated 2018/03/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of semi-inner-products to obtain a complete characterization of the norm attainment set of a bounded linear operator between any two real normed spaces. In particular, this answers an open question raised recently in [Sain, D., On the norm attainment set of a bounded linear operator, J. Math. Anal. Appl., 457 (2018), 67-76.]. Our results illustrate the applicability of semi-inner-products towards a better understanding of the geometry of normed spaces.