2020/10/06 by Geunsu Choi, Sun Kwang Kim
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Banach space #Bilinear form #Bilinear interpolation #Combinatorics #Computer science #Geometry #Holomorphic and Operator Theory #Mathematics #Pure mathematics #Regular polygon #Space (punctuation) #Statistics #math.FA #msc:46B04 #msc:46B07 #msc:46B20
paper · pdf · doi:10.1007/s00009-022-02007-4
published as Mediterr. J. Math. 19, 72 (2022) · 11 pages
arxiv created 2020/10/06 · openalex publication_date 2022/02/21 · arxiv updated 2022/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The main purpose of this paper is to study Bishop-Phelps-Bollobás type properties on c0 sum of Banach spaces. Among other results, we show that the pair (c0(X),Y) has the Bishop-Phelps-Bollobás property (in short, BPBp) for operators whenever X is uniformly convex and Y is (complex) uniformly convex. We also prove that the pair (c0(X),c0(X)) has the BPBp for bilinear forms whenever X is both uniformly convex and uniformly smooth. These extend the previously known results that (c0,Y) has the BPBp for operators whenever Y is uniformly convex and (c0,c0) has the BPBp for bilinear forms. We also obtain some results on a local BPBp which is called Lp,p for both operators and bilinear forms.