کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602601 1631171 2008 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the extremal structure of least upper bound norms and their dual
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the extremal structure of least upper bound norms and their dual
چکیده انگلیسی

Given finite dimensional real or complex Banach spaces, E and F, with norms ν:E→R and μ:F→R, we denote by Nμν the least upper bound norm induced on L(E,F). Some results are given on the extremal structures of B, the unit ball of Nμν, of its polar B°, and of B′, which is the polar of the unit ball of the least upper bound norm Nμ°ν°.The exposed faces, the extreme points, and a large family of other faces of B° and B′ are presented. It turns out that B′ is a subset of B; the set of tangency points of the surfaces of B and B′ is completely determined and represented as the union of the exposed faces of B′ which are normal to rank-one mappings. We determine sharp bounds on the ranks of mappings in these exposed faces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issues 8–9, 15 April 2008, Pages 1928-1938