2019/07/03 by Debmalya Sain, Sain, Debmalya
Mathematics · #46B20 #46G25 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1907.01955
openalex publication_date 2019/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the smoothness and the norm attainment of bounded bilinear operators\nbetween Banach spaces, using the concepts of Birkhoff-James orthogonality and\nsemi-inner-products. In the finite-dimensional case, we characterize\nBirkhoff-James orthogonality of bilinear operators in terms of the norm\nattainment set. This yields a nice characterization of smoothness of bilinear\noperators between Banach spaces, in the finite-dimensional case. Without any\nrestriction on the dimension of the space, we obtain a complete\ncharacterization of the norm attainment set of a bounded bilinear operator\nusing semi-inner-products, which is particularly useful when the concerned\nBanach spaces are smooth.\n