کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590576 | 1334968 | 2014 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Octahedral norms and convex combination of slices in Banach spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We study the relation between octahedral norms, Daugavet property and the size of convex combinations of slices in Banach spaces. We prove that the norm of an arbitrary Banach space is octahedral if, and only if, every convex combination of w⁎w⁎-slices in the dual unit ball has diameter 2, which answers an open question. As a consequence we get that the Banach spaces with the Daugavet property and its dual spaces have octahedral norms. Also, we show that for every separable Banach space containing ℓ1ℓ1 and for every ε>0ε>0 there is an equivalent norm so that every convex combination of w⁎w⁎-slices in the dual unit ball has diameter at least 2−ε2−ε.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 266, Issue 4, 15 February 2014, Pages 2424–2435
Journal: Journal of Functional Analysis - Volume 266, Issue 4, 15 February 2014, Pages 2424–2435
نویسندگان
Julio Becerra Guerrero, Ginés López-Pérez, Abraham Rueda Zoca,