Research on geometric structures of Banach and function spaces with direct sums

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400131
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Shinshu University
• Principal Investigator: KATO Mikio 信州大学, 工学部, 非常勤講師 (50090551)
• Co-Investigator(Kenkyū-buntansha): 斎藤 吉助 新潟大学, 自然科学系, フェロー (30018949) ; 田村 高幸 千葉大学, 大学院社会科学研究院, 助教 (30302582) ; 鈴木 智成 九州工業大学, 大学院工学研究院, 教授 (00303173)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: バナッハ空間 / 直和 / 凸関数 / uniform non-square性 / uniform non-[ell]-n_1性 / 不動点性 / バナッハ空間の幾何学的定数 / James型定数

Outline of Final Research Achievements

A sequence of results on some geometric properties, especially, the uniform non-squareness, uniform non-[ell]-n_1-ness, and p-convexity, etc. were obtained for direct sums of Banach spaces. Especially, the problem to characterize uniform non-squareness for direct sums of "finitely many Banach spaces" was solved, which was the most important problem of this research program. As corollaries of the result on uniform non-[ell]-n_1-ness we obtained characterizations of this property for direct sums of Lp-spaces and for strictly monotone norms on CN (N: superscript). Several results on James-type constant J_t(X) of a Banach space X were also obtained. (Some of the above results are in preparation.)

Free Research Field

関数解析学、バナッハ空間論