Biểu diễn nón Bishop-Phelps trong không gian hữu hạn chiều
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Abstract
The aim of the article is to study representations of Bishop-Phelps cones in finite-dimensional spaces under various norms. First, the definitions of cones in finite-dimensional spaces are recalled, accompanied by examples illustrating Bishop-Phelps cones with both empty and non-empty interiors. Next, the article explores the properties of Bishop-Phelps cones. Finally, these cones are utilized to represent foundational cones in finite-dimensional spaces, including the non-negative Orthant cones, Lorentz cones, and other related cones.
Tóm tắt
Mục tiêu của bài báo là nghiên cứu sự biểu diễn của nón Bishop-Phelps trong không gian hữu hạn chiều dưới các chuẩn khác nhau. Đầu tiên, định nghĩa về các nón trong không gian hữu hạn chiều được nhắc lại, kèm theo các ví dụ minh họa về nón Bishop-Phelps có cả phần trong bằng rỗng và khác rỗng. Tiếp theo, bài báo xem xét các tính chất của nón Bishop-Phelps. Cuối cùng, những nón này được sử dụng để biểu diễn các nón cơ bản trong không gian hữu hạn chiều như nón Orthant không âm, nón Lorentz, và các nón có liên quan khác.
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